Although I would question if multiple hours of daily labor isn't itself a significant demand pull? I assume everyone wants to free up time spent on monotonous tasks, but maybe this is wrong.
They simply didn't have the metallurgy.
A more interesting question is why China didn't kick off into an Industrial Revolution given that they effectively had all the same technologies and perhaps actually had a few more.
There were some cultural issues like considering philosophy more important than trades and technology. However, the general issue seems to be that demand and supply were balanced enough that there simply wasn't a huge incentive.
The Aeolipile was not a functional steam engine - it was essentially an unpressurised two-spouted kettle that span on an axle. It had no way of maintaining enough pressure (no valves) to do useful work and the metal working techniques of the day weren't good enough to contain useful pressure without exploding. Real steam engines only came about after people had spent centuries building cannons that didn't explode.
The first practical application of steam engines was pumping water out of deep coal mines (which the Romans didn't have or need) where it didn't matter if the engine was both underpowered and massive. Even after these engines became commercially viable, it took another 70 years or so for the engines to become small enough to be mounted on vehicles.
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.
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.
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.
The Romans were engineers par excellence.
They worked both steel and glass in this time frame. Look at how they built Pompeii for the local conditions. They built the Colosseum with lead clamps and rebar to prevent it from collapsing with earthquakes (it eventually collapsed because everybody stole the valuable lead as Rome failed). Their art was better than anything produced until the Renaissance happened. I can go on and on ad nauseam.
Romans most certainly did not look down on engineering and technology.