Why did Europe not see Roman-era numbers of men participating in battles until the 17th century?

For the same reasons why in many aspects, like technology, Europe till 17th century didn't really approach similar levels of technical advancement that it did in the Roman era1.

The evidence conclusively shows that the Roman world didn't just undergo a regular normal contraction which accompanies all dynastic collapses, but underwent a complete meltdown of societies. It truly was a dark age in terms of a complete loss of technical know-how, artistic and cultural sophistication, connections with the outside world, etc. Bryan Ward-Perkins archaeological work shows this quite clearly, as do reconstructions of data on industrial activities from the Roman period.[2]

What complicates such topics is that we retroactively apply the same hierarchical structures which exist today to the past. Thus it creates a cognitive dissonance when you stumble across time periods in which European states played the role of tertiary fiddles in the shadows of powers in the East.[3]

For centuries after the Western Rome imploded the only source of income generation was selling fellow women, children and men as slaves to the rich fabled lands in the East, a trade that was dominated by the Vikings, and also what served as the foundations of the Venetian wealth that built that gorgeous city. Europe had nothing to offer in terms of goods with which to trade, except people to be sold as slaves. And this wasn't a small time trade just on the fringes - coin hoards found along the banks of the Volga and in continental Europe indicate that it was equivalent to a modern day $250 billion industry [4]

Such a large scale naturally influenced the development and evolution of cultural attitudes and preferences. Why waste healthy men to be used as cannon fodder in tribal wars (which were in any case fought over extremely inane and petty issues) when you stood to make magnitude more selling those men as slaves in the East?

Such attitudes only began to pushed away when the European powers grew not to be just a collection of towns with huts of thatched roofs but of dominions in far away lands in the 17th century, just as colonial age was beginning.

Imperial attitudes began to sway the states as they now held far flung dominions across the world, and for that you needed men to be used as cannon fodders.

1 Check Bryan-Ward Perkin's Fall of Rome (2005). In case reading the book is not possible, he has several talks where he gives lectures thoroughly rebutting the idea of a romanticized transfer from Rome to Germanic tribes; https://www.youtube.com/watch?v=__HoBL_RD9w being one of his lectures.

[2] We get a sense of trade movements via the catalogs of ancient era shipwrecks discovered by modern day scholars. The data for this can be at an online repository of datasets kept by Oxford on Roman economy (http://oxrep.classics.ox.ac.uk/databases/shipwrecks_database/)

The key thing to remember is that the probability of a ship to sink over the long course of periods should be fairly random (a long period of time eliminates a exogenous shocks driven shipwrecks - like natural disasters for example). And that the probability of a ship to sink is same for each ship. So the movements in the frequency of shipwrecks are a good proxy for trade flows, with higher occurrence of shipwrecks pointing at a much larger number of ships floating at that particular period, and lower frequency hinting at a decreased commercial flow.

So when you visualize the data from the shipwrecks dataset, you get this.

Note that trade barely picked up after the 6th century, despite by the 8th century the Islamic world having established as the most richest and most dominant hegemony, controlling the arteries of the world.

And it is the same story when you look at data collected from Icelandic glaciers on lead isotopes. Lead is a very common byproduct of gold mining, and many other industrial activity, so in a way specific lead isotopes record the state of industrial activity. For a deep analysis of this, see Joseph McConnell et al, Lead pollution recorded in Greenland ice (https://www.pnas.org/content/115/22/5726)

[3] A large body of work has been done exploring and trying to create an accurate portrayal of what the Arabs, Persians and other members of the Islamic world during the 9th centuries onward thought about Western Europe. Despite being in close geographical proximity, most of the accounts from travelers and geographers have a very conspicuous absence of any mention of Western Europe, except a handful of superficial mentions and then quickly moving on to talk about other regions. This lack of any curiosity wasn't because the Islamic cities had no knowledge about Western regions - Muhammad al-Idrisi, an Arab cartographer from Ceuta who lived from 1100 to 1165AD produced extremely detailed maps and accounts of roads which spanned across the entirety of Europe.

This absence of any substantial mention of Europe among Arab accounts was due to the outlook among Arabs at the time that Western Europe represented intellectual backwaters compared to the level of sophistication the Islamic societies possessed. And this outlook broadly fits the archaeological findings on the nature of societies and empires that emerged from the cesspool of chaos that West Rome's collapse left behind (one might want to look at the works of Bryan Ward-Perkins on houses in Britain prior to Rome's collapse and post the event.

Peter Frankopan tells, "While the Muslim world took delight in innovation, progress and new ideas, much of Christian Europe withered in the gloom, crippled by a lack of resources and a dearth of curiosity." Al-Masudi, an Arab historian bluntly writes, that "West had nothing to offer."

Another dimension which showcases the declined status of European powers during this time is from imitations of Islamic gold dinars by European kings, as far away as Britain. Imitations of coins are a marker of the sovereign differentials existing at the time (and coinage since antiquity to the very modern day is a very large function of the sovereignty enjoyed by the entity which issues it - think about why a piece of paper on which you write 100 is worthless but a green colored paper issued by the US government is a safe store of value). We don't find imitations of Carolingian money ever. And the some of these imitation coins whilst being beautiful in some instances, were almost an exact replica of Islamic coins, down to even carrying Arab inscriptions! (See Briton King Offa's gold dinar).

[4] Explore Oxford's Dirhams for Slaves project.

A lot of this is down to differences in how the various states were organized. Rome was a highly centralized imperial state, with its own currency and taxation.

The states of Medieval Europe for the most part did not have a money economy. The Feudal System was basically their answer to how one runs a country and maintains a professional military (an absolute requirement in an era when cavalry was the dominant arm) in an agricultural society with little or no flowing currency to tax. Essentially everyone, at every level, paid their "taxes" directly in labor. A rich person was a person who had a large amount of labor owed to him, generally by virtue of controlling a lot of usable land.

It worked, barely, but it is simply a much less efficient way to run a state. Cheating by not providing all the labor due to those higher up the chain is much easier to accomplish, and the higher you get (and thus the more labor at your disposal), the tougher it becomes for those up the chain to extract their due from you by force. This is part of why they were called "The Dark Ages".

So in general, a Feudal society is always going to punch way below its weight, due to how inefficient the system is.

Basically, European "states" were all smaller than the Roman Empire, in reach and population for 1000 years or so after the fall of Rome. More to the point, they were mostly subdivided into feudal principalities for most of the period. Rome in 278 BC had better control of "half of Italy" than Paris over all of (or even half of) France in 1346 A.D.

At its height, the Roman Empire consisted of the modern Italy, Spain, France, Britain, the Benelux countries, the Balkans, and parts of the Middle East and North Africa, and other areas.

By definition, all these "European" countries were much "smaller" in size than the Roman empire. More to the point, they were all much smaller in population, wealth, and "governability," at least until the 1500s and the resulting enrichment of the Continent through the discovery of the New World. Also, by around 1500, the European countries wee starting to become real "countries" (where Rome was, shortly after 300 B.C.), as opposed to a collection of feudal states. Before that time, no European power had anything like the mass of the Roman empire, or its ability to field armies.

It's true that the European countries (mostly) increased in population relative to themselves from 1 A.D. to 1500 A.D., but they all decreased in population relative to Rome over that time period.

The other answers cover most of what is being asked here but I thought I should add that a major factor in what caused these inabilities was a lack of economies of scale. Whereas the Romans had highly organised production, distribution and retail of both consumables and materials, the Feudal era was highly decentralised. The Feudal era fiefs had only small scale local production, in both agriculture and materiel. Water was another major issue, water quality was poor, and cavalry especially consumed a lot of it. Whilst a lot of the water infrastructure put in place by the Romans remained but it's distribution was not nearly as effective as it is today. Agricultural techniques were primitive so irrigation required a lot of water in order to maintain even meagre crop yields.

Think of it this way: Is it more effective to have 1000 local blacksmiths managing not only the production of war materiel but also meeting requirement for producing local goods (say horseshoes, ploughs and the like); than to have 10 forges dedicated to producing only swords, shields, horse bits - etc. etc. ? Both a centralised government (e.g the Romans) and a Feudal lord may only be able to dedicate 10% of surplus production to a war effort but the 10% surplus of a centralised government is far in excess of the 10% of 100 fiefs.

This, as mentioned by others, is one reason why sovereigns could not support large armies, nor support them for very long. Most armies, even in the Roman era, often had to survive by foraging off the land, and this was only really achievable in the warmer months of the year. Texts like Livy and Pliny make repeated reference to the campaign season, which one would interpret as the spring and summer months.

This leads into another issue - transportation. Because the vast majorities of troops were foot levies, and there were realistically only a few campaigning months in a year, the time required for a levie to arrive in time for campaigning was very limited. Lines of communication were not only long, but they were poor, with messages being transferred via courier on horseback. This meant mobilisation took time. As the Romans not only in later years had professional standing armies but a strong martial culture throughout, mobilisation was efficient.

Troops travelling in the winter would suffer high rates of attrition: through starvation, desertion and death from the elements. An army could not forage in the winter, as there were no harvests, and what stores were available were usually holed up in the local lords castle. Sieges were a dicey proposition at the best of times, and an army laying siege to access stores in the winter was in dire straits indeed. The further an army advanced the longer it's lines of supply grew and the more vulnerable they become. Commanders would have to garrison these lines of supply and this in turn would affect combat strength.

Perhaps a better question to think about is - what were the similarities between the Roman and the Colonial/Imperial age logistical systems that allowed them to field such large armies so effectively? Perhaps rather than focusing on why medieval armies fielded so few troops, consider what enabled the powers of antiquity and the Colonial to project force so effectively.

In the case of the Athenians, it was their naval power, in the case of the Romans it was their road networks; later with the Imperial powers it was again the ability to project power using navies and the widespread expansion of the railroad that made large scale warfare a cost-effective proposition.

In the 1700s, a number of technological revolutions took place that allowed for sovereigns to field large armies. First of all the rise of the Westphalian nation state allowed for central governance of large economies and professional militaries. With the decline of feudalism, governments were again able to achieve the kind of economies of scale that allowed them to dedicate significant surplus resources to war production - a trend that continued for some time and culminated in the Great War and World War 2.

The advent of the railroad allowed armies to be mobilised and deployed quickly. This was probably the single most important innovation in military history to date since the domestication of the horse, the development of the ship (is there a better word than ship? Naval transport perhaps?) and the prevalence of the Roman road network. It improved lines of communications and allowed a general to control forces over a greater geographical area.

Compare the levels of command and control. Fiefs were essentially little micronations often speaking different dialects; feudal lords under one liege may actually be rivals on their own turf. Being able to effectively dictate and command large armies requires that a general can communicate quickly and effectively with his troops. As rival fiefs may have their own agendas or may not wish to assist a competitor achieve glory or curry favour with the monarch, discipline varied widely. Consider the evolution of the hierarchies in modern militaries, their evolution from the early standing armies, and compare to them Roman military organisational reforms, like the Marius reforms. Then consider the flattened hierarchies of the medieval eras, and compare the performances across all three.

The majority of a feudal army would have been made up of peasant conscripts who were pressed into service with very little training and very little motivation to fight for a feudal lord who was likely a brutish taskmaster who profited off the backbreaking labour of his subjects. Whilst the weapons of the Imperial days did require steel and a good deal of it, on a per capita basis, the amount steel required to be effective was small, and the available production of steel was relatively high.

Compare this to the average heavy infantryman of the dark ages: His weapon was all steel and very likely to break in combat, his armour was steel or iron if he had any at all and the available production to support it was quite low. Apart from the richest lords, most soldiers and knights had to pay for their armour out of pocket, or seize it from the dead. There would have been little uniformity as all items were handcrafted, and only the richest soldiers could afford tailormade armour.

Keep in mind that even by the Napoleonic wars, the size of armies only really began to increase by the end of the 1700s. However from an organisational point of view, logistics and command and control hadn't begun to improve very much. Tt Austerlitz, the number of troops who actually fought were sixty and eighty thousand respectively between the Allies and the French. Though the Armies fielded by Napoleon were as a proportion of population not considerably larger than those of a few centuries earlier, his disastrous invasion of Russia shows what happens to a large army when the infrastructure isn't there to support it. After the pyrrhic victory at Poltava and Muscovy, the Russian winter decimated his Grand Armee. Without the ability to both supply and transport it, it fell apart from attrition and desertion. This demonstrates quite clearly that armies of a certain size require a base-line of logistical support.

Even as we look at the American Civil War we can see even with technological factors accounted for, the ability of the minds of the day to effectively control large armies of a million men upwards was very low. Incredibly high casualties, military blunders were all underscored by a lack of effective command and control and discipline. In World War I, it was quite obvious that commanding armies of such enormous sizes, technological and logistical capability was far beyond the ability of the commanders of the day. Only after four years of total war and immeasurable bloodshed were the commanders of the day able to develop the tactical and logistical solutions to solve the technical challenges they faced. However, if we look at a number of the smaller campaigns in both the Civil War and World War I (for example The War in the West (Civil War) and the Palestine Campaign (WW1) we see that commanders were quite capable of managing their forces and pulling off quite technical battles of manoeuvre and combined arms long before these were integrated in army wide doctrines by the end of the the respective wars.

Only in the second world war did we see truly vast numbers of soldiers being controlled effectively by the Allies and the Germans.

From that high point now we've seen actually a great decline in the absolute size of armies to the point where today even the U.S combat forces only number around 350,000. It seems likely that there is an optimum size for an army beyond which command and control becomes difficult and the number of support personnel required to support it balloons out to unsustainable numbers.

In short:

• Economies of scale: Sovereigns of Feudal states could muster resources far less effectively due to the inherent inefficiencies in feudal economies due to a lack of economies of scale
• Logistics: Both the Roman Empire and the Colonial Empires of the 1700s understood how important transport networks were and invested heavily in them. In the case of the Romans it was roads, the European Imperials it was railways.
• Discipline: Both the Europeans and the Romans had professional standing armies who were motivated to fight and could expect a good reward for decent service.
• Command and Control: The Romans had centuries of practise in mobilising, deploying and fighting with large armies. The Europeans had less experience and were far less successful at doing so, but they had superior technological advantages such as the railroad and the telegraph that overcame many of the shortcomings.
• Social: The societies of both the Romans and the later Europeans were centralised nation states with strong social hierarchies that rewarded loyalty and punished insubordination (to an extent)
• Technological: The doctrines of the Middle Ages called for heavily armoured cavalry and infantry without the requisite levels of industry to support them. The Roman armour was mostly hardened leather, and they still used wood as a large component of a number of their weapons. The European armies did not requires the same amount of steel per soldier as the advent of gunpowder had made plate and chain mail obsolete.
• Environmental: The effects of the Black Death would've affected the available numbers of manpower reserves and surplus agricultural production required for a large scale war effort.

Things to consider:

• First, it is difficult to assess the size of armies in the Middle Ages. Roman troop strength is relatively easy to calculate by knowing the legions involved (the legions usually having the same size), but medieval armies usually had no such regularity.
• Smaller polities (kingdoms and or counties instead of empires) meant smaller population, and smaller armies.
• Switching from infantry based armies to cavalry based ones; which were smaller but more expensive and (usually) powerful.
• Feudalism, with two issues:
  • a nobleman could disagree with his liege's policy and refrain from sending troops when requested, or send only the bare minimum.
  • even in the case of all the noblemen agreeing with the King's orders, we can count that each noble who provided troops kept a sizable reserve defending his castles. Roman organization meant that, when needed, entire sectors of the frontier were left almost undefended (and in some cases, some provinces were abandoned).
• From 1350 onwards, the Black Plague.

Also, specifically for the Battle of Crecy:

• This was the ninth year of war, so some attrition would need to be accounted for.
• Not all of France was directly controlled by the French (I very much doubt they had access to levies from Gascony or Brittany).

And to end, a list of some battles in the Middle Age who were, indeed, quite crowded.

Battle of Tours (year: 732)

• Low estimate: 15.000 Franks vs 20.000 Arabs.
• High estimate: 80.000 Franks vs 80.000 Arabs.

Battle of Manzikert (year: 1071)

• Low estimate: 40.000 Byzantine soldiers vs 20.000 Turkish soldiers.
• High estimate: 70.000 Byzantine soldiers vs 40.000 Turkish soldiers.

Battle of Alarcos, and link to the Spanish version, with force estimations (year: 1195)

• 25.000 Christian soldiers against 20.000 Almohad soldiers.

Battle of Mohi (year: 1245)

• Low estimate: 25.000 European soldiers vs 25.000 Mongol soldiers.
• High estimate: 80.000 European soldiers vs 80.000 Mongol soldiers.

Siege of Baghdad (year: 1258)

• Low estimate: 120.000 Mongol soldiers vs 50.000 Islamic soldiers.
• High estimate: 150.000 Mongol soldiers vs 50.000 Islamic soldiers.

A major reason would be logistics. It's not all about population sizes.

The strength of an army is constrained not just by its manpower sources, but also by the logistical infrastructure available to pay for, feed, and equip it. The Romans in particular were much better at this than the feudal states of Medieval Europe, which tended to be quite factious and decentralised. Consequently, for centuries after the Roman military system disintegrated, the capacity to field and support forces on a Classical magnitude became mostly absent in (Western) Europe.