Yes. Up until the 12th century, which is where the Middle Ages really stop, European armies were really distributed along the lines of Roman Provinces. The national divides and then Feudal divides really ran very closely to the Old Imperial Frontiers.

I've been holding off in the hopes of providing a good answer; I don't think I have a good answer, so I'll provide the best poor answer I can.

Let me restate the question slightly, since I think the existing answers have been influenced by distractors in the current phrasing of the question.

What factors influence the relative military strength and distribution of vassals in a feudal government.

The question was driven by the observation that Japan chose to keep strong vassals near the court, while China positioned the strongest vassals at the periphery. European monarch invested very strong marcher lords, while keeping those closer to the capital weaker. What factors influence each choice?

I don't expect that there is a single clear answer - the point of the question was to examine alternative hypothesis that might account for the relative strength of vassals on the border vs the periphery. If there are multiple viable factors, we can adjust the strength of the [original hypothesis]. If we can't develop a predictive model, perhaps we can create an analytical model that provides a number of factors to consider when analyzing similar situations. Unfortunately, that puts us in the realm of a list question, which is usually a poor fit for H:SE. I'll mark this answer as community wiki and encourage others to contribute list factors.

Some factors we're pretty sure influence relative military strength of vasssals over geography.

• External threats - Marquis vs Count is a design pattern resulting from a persistent, strong external threat - In addition to the French example, this is clear in the English Marcher Lords. The crown invests Marcher Lords with more power than would normally be tolerable, but positions them adjacent to external enemies; the Marcher Lord cannot rebel against the center without exposing the rear to the external enemy.

• Crown military strength - An old acquaintance introduced me to the generalization (Possibly from Durant, although I cannot confirm) that one of the critical differences between English and French history was that the French king controlled forces that were tiny fractions of his vassals, while the English king controlled military forces that were closer to the strength of the vassals. The English King could hope to fight a single rival so long as he didn't fear a coalition of Barons; the French King had no hope of defending himself, and had to politic his way out of the problem. The French king had an incentive to keep all of his chief vassals close, because his politicking relied on rapid communication; the English King had an interest in keeping the vassals dispersed in the hopes of preventing communication among potential rivals. I don't know if this generalization holds up, but it suggests that communication speed may be a factor in the strength of vassals.

• Innovation, particularly with respect to the relative advantages of offense and defense. Alfred's strategy of empowering burghs would have been absolute folly during the Anarchy; castles change the rules.

• bit of a stretch, but Bad King John changed the nature of English politics by building a coalition of the crown and the peasantry to oppose the Barons. Although his coalition didn't affect relative military strength, it did change the role of the crown throughout English history, and quite frankly shaped the construction of the English Empire and the American Republic and Empire.

• Fortune - I'd prefer to keep this factor on the bottom, but history is full of times when the relative strength of various vassals is affected by ill fortune - a famine, a plague, an earthquake, a Tsunami, etc. Suddenly the relative strength of the vassals is dramatically altered. I'd also put in this category charisma. Alfred of England didn't succeed because he tried anything new, he succeeded because he was simply too stubborn to notice that he'd been defeated. Some combination of persistence, charisma and luck allowed him to triumph where others had failed. One leader may propose strengthening one vassal and weakening another and fail, while another may make the same proposal and succeed.

Like I said, this is not what I consider a good answer; I can't prove or disprove the original hypothesis but I hope that consideration of the viability of alternatives will weaken the original hypothesis - kind of like providing reasonable doubt in a trial.

No, but people truly thought they were.

Any reading of medieval sources shows us that Medieval folk truly believed that their society was structured by God. They weren't completely naive and knew that their institutions were imperfect, but they were confident that whatever deviations there were from the ideal were temporary and would be put right by the next king, emperor, or pope. If all you read is the literature and historical accounts, you might easily conclude that the simplistic feudal model so often depicted in modern movies and books was real.

But any examination of source documents - tax records, muster rolls, private correspondence, and such - reveals a much more complex reality. So much so that many scholars today reject the term "feudalism" altogether. That might be a bit extreme, but at the very least the term deserves reexamination - for example, in the book "Fiefs and Vassals, The Medieval Evidence Reinterpreted", by Susan Reynolds. (https://global.oup.com/academic/product/fiefs-and-vassals-9780198206484?cc=us&lang=en&)

The reality was this: medieval society lacked the material sophistication for rulers to fully order their realms. Communications were too slow, literacy too rare, institutions too weak, and national identities too ephemeral for any sort of political system to be effective. Rulers were constantly forced to take ad hoc measures, and their subjects took advantage of the countless gaps in the social structure to advance their own interests. Titles, offices, and even laws could not be assumed to be effective.

I suspect that it is due to this extraordinary amount of uncertainty in medieval society that people were so willing - perhaps desperate - to believe that the feudal system was really at work, ordering the current society and just waiting to be perfected by the next Charlesmagne or King Arthur.

So, No, armies (and other instruments of power) weren't truly organized by a coherent model. They were constantly in flux, based on not just the factors that are suggested in the question but religious ideals, mercenary motives, dynastic considerations, and especially the personalities of the leaders.