Under that sort of logic, mining should be labour intensive as well (which it is, unless you spend the capital to get drills or quarries). And cantr doesn't handle slaves very well, for some reason young people don’t fear death, maybe its their belief in coming back as something else?

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But I think we can agree that cotton needs to be more intensive (and require more equipment to process) than hemp, even with special equipment.
Just had a thought, could you restrict building a cotton picker to areas that only require cotton (a little obvious sorry), but instead of getting cotton from operating the machine you would get "cotton plant" (I'm better with numbers than names sorry) which you would receive quite a lot of cotton plant for ... but you would also have to build a second machine indoors to process that "cotton plant" into either fibres or cotton.
Both machines would be resource intensive to set-up. But the pay off would be making cotton cloth at 200g per day? Still a fair bit less than Hemp (With no special equipment), but 4 times more than if you did it by hand. Is that a solution you'd be happy with?