In fact, growing cotton with slave labor is what prevented the south from entering and benefiting from the industrial age. Plantation owners would rather sell cotton as a raw material to the industrial north, as well as Great Britain and France. They would rather pocket the profits, than pay for developing any local cotton fabric weaving industry in the south.
So claiming that the industrial revolution had made slaves unnecessary is untrue. If anything, it is part of the false 'revisionist history', spread by the south in the decades after 1880, that claimed the Civil War was not about slavery, but about state's rights.