Why did the steam locomotive take so long?

That's because you look at the problem the other way around. You are accustomed that technology develops lightning fast. In 2000 very few people had internet access, and a lot of business was done without computers. Now, a mere 20 years later, in 2021 everybody has internet access and business cannot be done without computers. (This varies per country, of course.)

That became only possible with advantages in technology, and the infrastructure had to be in place first. Without affordable computers, you wouldn't have a computer to connect to the internet. You couldn't connect to the internet if you didn't have a connection first, even if you had a computer. Even so, in 1997 internet access was very expensive. My first browser was Lynx. To connect, I used Trumpet Winsock. Lynx didn't show images. That was faster and cheaper. You'd connect, download or find the info you needed real quick, and disconnected. Yes, it was in 1997 that expensive. I'm not even talking about flaky connections, it was quite normal you had to dial in many times before a more or less stable connection was achieved.

The same goes for the steam train. First, people had to come up with the idea of vehicles being propelled by machines. Don't forget, nobody had seriously thought about that before. It was something completely new.

The concept of rails did exist, mines used wooden rails. But wooden rails aren't good for trains. You need steel rails. Making steel was very expensive back then.

After the invention of the steam engine, people created affordable water transport with barges (pulled by horses), by building canals. That made transportation of coal and iron ore much cheaper. With that now cheaper and more plentiful steel, economically affordable rails could be build.

Only then it became technically and economically possible to think about building trains. People were afraid of that new highly dangerous technology, many people - not necessarily uneducated - thought passengers would suffocate travelling at such dangerously high speeds.

You need the technology, it must be economically feasible, and the popular mindset must be there. Only then an invention can take off.

If you know 2 variables in math, you can figure out a third. With those three, you can more quickly find a fourth, and so on. The same goes for technology. Once the steam engine was invented, it led to other inventions, for example machines that very accurately measured and reproduced metal parts. You need that technology in order to build locomotives. All that takes time. Quite a bit of time, but progressively less so between inventions.

That's in a nutshell why it took a century to use steam engines for locomotives, and less than 50 years before the Internet really took hold.

(Yes, I know, in The Netherlands they used extensive water transport and windmills for centuries already. But they didn't invent steam engines or railroads.)

In addition to the excellent answers by Fred and Lucian, you also need to consider the economic situation at the time and the existing transport infrastructure.

The Industrial Revolution in the UK is generally regarded as beginning in the mid-eighteenth century. By then there was already a transport system that provided for the needs of the country. In 1707 the Turnpike Act had been enacted and this was followed by a growth in the road network. By the 1750s an extensive stagecoach and flying waggon network had been developed. At the same time, the rivers were being made navigable, and the canal network was starting to be developed. These were supported by local farmers providing food for both the horses and the people. Coaching inns were already there. Mills and factories were built alongside the rivers, canals and roads. Everything was set up for road and water transport, there just wasn't anything pushing for railway development and the expensive research that would be needed to make it work.

It wasn't the Industrial Revolution was well underway that there was the money and the market for what the railways could provide.

As the adage goes, necessity is the mother of invention. If there isn't a perceived idea, it doesn't get invented. Things get designed to solve a particular problem. There is also the issue of the state of technology at a given time.

The first issue, was the earlier steam engines were not particularly powerful, so steam engines had to evolve before they could become powerful enough to become a locomotive engine.

The second issue was rail and wheel design. We now take it for granted that wheels used on railroads are flanged, but the metal wheel-rail configuration wasn't always this way. Initially wheels were straight, like cart wheels, and rails had grooves for the wheels to run in. This system used a lot metal in comparison and wasn't capable of bearing heaving loads. Putting a flange on the wheels and no groove in the rail was a vast improvement. Deciding on the profile of the rail was the next improvement.

The third issue was material used for wheels, rails and steam engines. For rails, cast iron was initially used and it was unsatisfactory. Cast iron was brittle and readily broke. Also, the rails were made in short lengths and were uneven. It wasn't until 1820 when rolled wrought iron rail was available that rail technology improved. This resulted in the expansion of railroads between 1825 and 1840. Making rails out of steel was the next significant improvement. This was then followed by limiting the amount of sulfur or phosphorus in the steel used for rail and wheels.

The steam engine was invented around the start of the 1700s

Thomas Newcomen's 1712 atmospheric engine — itself an improvement on Thomas Savery's 1698 steam powered pump, known for being prone to explosions — still presented one major disadvantage:

80% of the steam used by the engine was wasted

which was only solved by James Watt's critical addition of a separate condenser in 1765; thus, over half a century had to pass, just for this much needed improvement to occur, thereby moving our timeline from the start of the eighteenth century, to its middle.

Even so, the engine was still stationary, meaning that its colossal weight was yet a non-issue, given its initial or primary purpose, namely replacing older hydraulic equipment, employed mainly by the milling and mining industries, whose basic design remained virtually unchanged since antiquity.

It is only when the question of mechanically powering moving vehicles arose, that this fundamental problem was first brought to the forefront; but, for that to be even considered, yet another half a century had to pass, during which time, Watt was still busy perfecting the engine; meanwhile, important breakthroughs would eventually follow, including those by other inventors, such as John Fitch's 1787-90 steam-powered boats.

One such milestone was Richard Trevithick's 1801 high pressure engine, aptly called the Puffing Devil, a precursor to his 1802 experimental Coalbrookdale locomotive and 1803 London Steam Carriage, representing

the world's first self-propelled passenger-carrying vehicle.

One of the reasons behind said delay was Watt's legal patent expiring in 1800; indeed, the two men were fierce competitors in the engine-building market. It is within this wider historical context that

on 21 February 1804, the world's first railway journey took place.

Since the other answer mentions computers, think of how the furniture sized computers of the Second World War, used for cracking German Enigma codes, had to wait decades for the modern PC to evolve into something recognizable today as such.