There's basically two camps on the issue of wildlife farming. One is that wildlife farming can help conservation. One proposed reason is that farming increases supply, reduces prices and deters poaching. So not surprisingly, it often mooted as a policy to employ if poaching is a major conservation problem.
The other camp argues that it is a measure that exacerbates extinction risks. Legal trade provides a potential vehicle for laundering. Some also worry that any stigma associated with consumption by bans, will end and demand rise. The last point is a little tricky, because stigma effects are a little difficult to identify and measure. And it's also often asserted it can't possibly work because shooting wildlife in the actual wild, is much cheaper than raising than on a farm or ranch.
Anyway, the whole point about alligators, is that it is a conservation success story, poaching has not resumed but has collapsed, and it is a rare empirical case where farming and hunting coexist. Instead of having to come up with various theoretical models, we can actually look at what happens.
The basic message is that we tend to be far too pessimistic about the ability of wildlife farming to contribute to conservation. None of the issues identified in the arguments above hold. Prices haven't collapsed despite massive increases in output, while poaching has for all practical purposes disappeared.
There are some good reasons why. Most of the positive conservation effects are felt through the non-price paths. Leather-manufacturers switched to legal skins because of volume and quality reasons. Consumers switched to legal products out of 'green' motives. And some of the reasons for pessimism didn't hold. Pessimistic theoretical models tend to assume the wildlife is open-access. This is an extreme case, which is known to lead to over-harvest. It lead to the almost complete extinction of bison in America, moas in NZ by early Polynesians and also, the collapse of several species of whales in the 20th century. It shouldn't come as a surprise, that if your model includes an open access condition, you'll get a decline in wildlife. That's going to hold under a variety of conservation policies. It practically makes the assumption of farming redundant. And no, it didn't actually apply in the case of alligators.
Of course, this isn't arguing that wildlife farming is a general solution to conservation problems. But there could well be more cases where it could support conservation, it we weren't quite as pessimistic about its chances.