I see a strong counter-argument in their advanced knowledge (and industrial-scale use) of hydro power. Are you familiar with the Barbegal mills?

What I think could have been a considerable factor that is rarely discussed is how "cosmopolitan" power structures appear in the late empire: someone makes an exceptional military career, gathers loyalty in the legions currently stationed in whatever corner of the empire he happens to serve, a few years later he's one of the contenders for emperor in the next civil war. But the economic development of the regions the "players" are associated with (if they even are associated with some specific region) doesn't seem to be a factor at all in that game.

A few centuries later feudalism and successors had military power (and with it political power) tied much closer to actual land and its economic power. This certainly did not directly lead to politics trying to foster industrial progress, but I can easily imagine how one form of stability (some hierarchy of lords stable for generations) could set up the prerequisites in a way the other form of stability (one seemingly eternal super-state but in an endless state of internal strife as the only form of meaningful achievement) would not.

The British Empire too had relied on slavery until well into the nineteenth century. By which time the Industrial Revolution was already underway.

There were some significant differences. For one thing, slavery was not legal within Britain itself, which is where the industrial revolution occurred. While no doubt slavery abroad meant that some luxury goods like sugar or tobacco were cheaper than they otherwise have been, there weren't slaves working the fields to make food and weave clothes in Britain itself.

There's a whole lot of research to show that the cost of labour in Britain in the 18th century was far higher than that of continental Europe - several times higher. And that this high cost of labour is what spurred on innovation.