The vast amounts of labor (including slave labor) might have been more of a hindrance than a help. It takes a labor shortage to create an incentive for innovations that increase productivity.
I have read that argument before. And I totally get that Rome as it existed did not have the right conditions for a British industrial revolution, but it did check many boxes and you could play out many what-ifs had it survived a bit longer. What if slave revolts caused labor prices to sky rocket, what if deforestation had continued, what if some other nice use case for steam power has caused an innovation s-curve on that tech, and so on. History is weird and so are humans. It could have been some hot new toy or religious ritual of the spins that did it. Saying it had to be coal mining is pretty baseless.
It also could have even driven more slavery, like the cotton gin did to the antebellum south.
Indeed. Why bother developing engines to power turbines for your ships, when you can just chain up a hundred slaves in the galley and give them oars?
Galley oarsmen in the Roman empire were mostly paid professionals, not slaves. The images you might have seen in cheesy old movies aren't historically accurate.