This is probably correct. When the north and south fought in the American civil war, the northern states had a highly industrialized economy while the south was almost entirely agrarian. In fact, perhaps because of the dichotomy between the two regions, the north may have been under even more pressure to mechanize. They had 5x more factories there than in the south, and more than twice the rail mileage.
It's an interesting thought, but I've always heard that the cotton gin was actually responsible for propping up slavery in the US south, as counter-intuitive as it that may seem?
That sounds like https://en.wikipedia.org/wiki/Jevons_paradox, and in fact the article has this snippet: "The expansion of slavery in the United States following the invention of the cotton gin has also been cited as an example of the effect.[12]"
True, but the cotton gin only made processing cotton more efficient. It didn't help in actually growing or harvesting it. So unfortunately, more efficient processing did encourage more production by manual (slave) labor.
One interesting factiod¹ is that a root cause for the transatlantic slave trade was that Africans were the only plantation workers that didn't die of malaria after a few years. Both local natives, and imported Europeans kept dying off.
¹ As in, I've seen it stated as fact, but am not sure how true it is
However, slavery didn't prevent (or even effectively compete with) the invention either, like the OP and many others have suggested about Roman slavery
This is the correct answer. Most answers here focus too much in technology, but forget about economics. And even if they had more technological advances, it is difficult for a technology to became competitive when you are competing with slave labor. And if slaves are supposed to operate your technology, this also creates several technological restrictions: slaves always will treat their working tools badly, so you cannot have machines with delicate parts.