In short, the best application of Hero's invention was still a machine that was inferior to a work of a single person while necessitating far greater initial costs and substantial costs of operation (fuel and maintenance), as explained by u/wotan_weevil in this thread, that it also references the obstacles to the industrialization in the antiquity presented by u/restricteddata and u/haf3clipse and the detailed explanation why it took much more than steam engine to bring the Industrial Revolution by u/LuxArdens.

The aeolipile or Hero's turbine itself, it has pretty little in common with the concept of a steam engine that gained popularity in 18th century. From the technical standpoint, it is a reaction machine (it operates using the force opposite to the force of the reaction mass being propelled in the opposite direction with the reaction mass being the steam) and thus is essentially a rocket engine rather than a reciprocal steam machine.

The main problem with the Hero's turbine is, as already noticed, a significant lack of scaling. First, to operate anything, aeolipile needs to propel itself i.e. move the entire assembly minus the support. This is easy to achieve in a small toy, but as soon as the size of the engine and thus its mass would have rise, more and more energy would have been needed to move the entire engine, before anything was even powered by it. Furthermore, as the steam engine utilizes pressure, it needs to be made of a substantially durable material to generate adequate power. Roman metallurgy was not bad, but it did not involve technology allowing for predictably consistent and what is more important, uniform steel. Whenever high pressures are involved, all pressurized containers must be as uniform as possible, because if there is one structurally weaker place, it doesn't really matter how durable the rest of the boiler is, as it will likely rupture in aforementioned location, as pressure of the gas is distributed more or less uniformly. And such level of steel manufacture was possible only around the time when the first steam engines were made.

Fueling of the device is also highly problematic. Given the configuration of aeolipile, one would need to locate the heat source outside of the engine and provide the adequate clearance for it to spin freely, what also means substantial losses of heat. It could have been alleviated by changing the sphere to a horizontal cylinder enclosed in the middle in some refractive chamber, but this would still be not enough. Furthermore, as this is a reaction engine, the operation would have quickly deplete the water inside. To refill the aeolipile, one would need to wait until it cools down enough to not start spinning when the water is added and then heat it again. This means frequent, long periods of downtime, severely reducing already dubious gains from the adoption of the engine, not to mention waste of fuel that was not free, either.

Now, there is of course the matter of the suspension that in this particular configuration would have required extremely durable and precisely made bearings to decrease friction. And that would be as difficult as making the material for the device itself i.e. completely beyond human technological capacity for the next 1700 years or so. And last but not least, regulation of the speed or stopping the machine would have been impossible save for manipulation of the fuel supply (that is imprecise and has a significant lag) or by introduction of the clutch and gears assembly of complexity rivaling that used in the modern automobiles (read: unavailable to people at the time, at least not on a wide scale).

Aeolipile was also very unlikely to become a starting point for a modern concept of a steam engine that operates on completely different principles and uses the differences of pressure (including partial vacuum) that was a concept unknown by ancient people in the Mediterranean region despite Ctesibius' forays into pneumatic and hydraulics in 3rd century BCE. This area of physics has been developed only in early 17th century (with Evangelista Torricelli being usually credited with the most crucial work on the subject).

If we consider all of these drawbacks, we can easily see that it made absolutely no sense to invest in this technology, as Romans already had much better equivalents available in the form of water wheel and horse mill, both being extensively used for at least three centuries. They were cheap (simple and made primarily of wood), relatively easy to make by ubiquitous carpenters, easy to scale to a substantial size, very easy to regulate (by driving or slowing the animals and operating the locks on a stream). And indeed, both water wheels and horse mills were commonly used to operate large millstones, lumber mills, forges and similar devices since and remained so for more than 1500 years (windmills and water mills were still operational in rural Europe, especially in its eastern and central parts as late as the first half of 20th century).

So, to sum it up, even an operational, efficient steam engine alone would not amount much to anything. The Industrial Revolution was, for all intents and purposes, a literal revolution that involved many changes on economical, social and technological levels. In short, Greek or Romans around 1st century AD did not have cultural or economical need for such a complex machinery, because the application of animals and relatively complex machines, such as treadmills and waterwheels that, supplemented by the muscle power of slaves that was ubiquitous at the time covered all the needs local societies might have required. In other words, any steam engine based on the concept of Hero's turbine would have been more complex and thus far more expensive, dangerous and ineffective in comparison with what Greeks, Romans or Egyptians have already been using on a daily basis.