> steam engines only came about after people had spent centuries building cannons that didn't explode

That's an interesting insight. I had not thought about the possibility of a scientific understanding of pressure developing prior to the steam engine. If you have some pointers to read up on this, I'd love to learn more.

Also, there were demands for pumps in antiquity, particularly in hydraulics. Lot's of labor was invested in building aqueducts and underground waterways. I always saw the Aeolipile as a tech demo showing that heat can be used as a power source for mechanical motion, but this is probably because I live after the steam machine, knowing it's true potential. I've long wondered why the idea wasn't expanded upon by the Romans or later the Greeks or Egyptians, but I suppose it wasn't convincing enough on its own.

I don't have specific links to this but it's more general reading of tech / military history over the years. I'd love to see a definitive study of the tech tree behind steam engines, but I do know that making bullets/shells precisely fit gun barrels took a long time, and this is analogous to making pistons in engines that don't lose pressure. The first mine-pumping steam engines were the size of small houses and stupidly inefficient, but, assuming lots of coal, they were still cheaper than having people / animals working water pumps all day. And they provided a good opportunity for engineers to properly iterate the technology with commercial pressure. They had a lot to learn though trial and error about how to optimise the things, e.g. adding condensing chambers that separated out initial water heating from power generation. This was all way beyond what the Romans could have achieved.

As you say, with retrospect we can see the Aeolipile as a tech demo, but at the time it was an interesting novelty with zero practical application.

Historians have come up with a lot of theories. There is no way to answer for sure though. General thought is they didn't even try because they had slaves they could force to do the hard labor, so there was not point. England developed steam engines in a world where slaves didn't exist. The Romans (their blacksmith god was disabled) also didn't value technology as a society like England did, and so they mostly didn't try to develop technology (except as it related to winning wars - anyone who wins wars was a big deal)

However it isn't clear if the Romans could have developed the metals needed even if they tried. There are a lot of parts to better metal alloys that they didn't know and trial and error is a slow process when you don't have why something didn't work.