That is a factor too. Slavery is expensive because you have to feed the slave even when they are not working. Same problem applies to using horses, they eat even where the fields are plowed. Machines sitting idle do not cost additional capital (other than taxes) - of course machine sitting idle don't make their payments, but you can arrange those terms with the bank.

Before the cotton gin, wool was more popular because it was less labor. (I'm not sure how silk and flax fit in, but all have their own labor intensive parts pre mechanization). By making cotton cheaper, the labor needed to separate the seed from the cotton was much less and so it was more competitive with others despite the high labor costs elsewhere.