The sugar culture of the Caribbean probably just wouldn't develop in the absence of the Atlantic Slave Trade. Working in sugar can fields in an endemic yellow fever region was just too brutal. The mortality rates among African slaves were far too high for any free population to tolerate, particularly when one remembers that Africans often had some inherited immunity to yellow fever that Europeans lacked.
The Spanish colonies were not such an exception, first because they were settled before yellow fever arrived from Africa and the populations were able to slowly build immunity in ways that new arrivals from Spain lacked, and second because the Spaniards in question weren't working in sugar cane fields. The Spanish territories in fact produced very little sugar until late in the day, when African slavery became more prevalent.
The American South, on the other hand, could absolutely be settled by free Europeans. Both the coastal colonies, with their tobacco cultures, and the later Mississippi Valley territories, with cotton culture, were inhabited by plenty of European farmers, along with the African slaves. The slaves were needed to enable the reproduction of a gentry lifestyle by the elites who established and governed the colonies. Free farmers could have grown the cash crops but would have wanted their own land and a decent share of the profits of the work.