For example, steam-powered battering rams or cannons would arguably be better as siege weapons than catapults or trebuchets, the rotational nature of the aeolipile might inspire better chariots, etc. They might have been developed further given the long "lead time" since its invention until the Industrial Revolution. What were the impediments towards their wide acceptance and employment in various fields of human interest?
There's a notion that the Greeks had discovered steam technology but did nothing with it because they had slaves. It seems to have been originally proposed by Toynbee in his unabridged Study of History, but I think it's in Howard Zinn as well...Anyway, I have answered the question about why Hero's Engine couldn't have done real work here. The same problems the Greeks had in producing a heat engine that would actually save labor, not simply spin around, would have been also encountered in making steam catapults, steam cannon, and steam battering rams.
They would have needed a pressure vessel, a boiler capable of holding a lot of steam under high pressure. That would have been difficult: even in the 18th c., almost all steam engines worked by condensation. Steam at quite low pressure ( perhaps as much as 7 pounds/square inch for the Boulton and Watt ones, less for the Newcomen type) was let into the steam cylinder, a valve was flipped and the steam condensed, and the resulting vacuum resulted in 14 psi of atmospheric pressure actually pushing the piston down. Higher-pressure steam was thought to be very dangerous, and high-pressure vessels capable of holding it were thought risky well into the 19th c., even after Oliver Evans had shown the advantages of using it. For good reason- like a pin popping a balloon, a weak spot in a boiler under high pressure can cause the whole thing to quickly fail and the results are catastrophic.
There would have had to be tight tolerances, for the large valves needed to handle the steam to make a cannon work, or for the sliding sections needed for a battering ram. Those parts would have had to be fitted by hand. Boulton and Watt could gloat about having a workman able to file a piston to fit a cylinder within the tolerance of a worn small coin, perhaps a millimeter. To make a sliding seal, they would fill that gap with combinations of old greasy rope, greasy wool, and leather. And that was to hold only 7 psi or so: a high-pressure engine needs about ten times that or more ( the higher the pressure, the greater the efficiency), and needs far closer tolerances and much better sealing materials.
There is a great deal more to making an invention work than simply sketching it. Some of them need a web of supporting technology, sometimes just one key invention, in order to be developed. The Greeks didn't have much of that yet.