I don't think that's true. I think apex predators have more regulators than alligators do in Florida, and most apexes are not prolific breeders, so they don't fit into this category, not in the suburbs. In addition, the abundance of alligators thin out large-mouth bass, which are a popular sport fish in Florida. As for the smaller reptiles, there are other predators that are getting edged out by the abundance of alligators.
They did get rid of the Muscovy ducks, which were mean and nasty. But I don't think it was a good trade off.
I know the correct thing to say is to let gators be gators, but at some point any species grows beyond it's feasible limit. In addition, the naturalization of suburban Florida lakes gives then nesting places in areas near people. You can argue that we were wrong to invade and transform their landscape, but the fact is we did, and now nature has to adjust to us, not the other way around. I understand it's not fair or right, but it is the only real option. Florida needs to aggressively cull the number of alligators in suburban areas, because without predators to limit them, the ranks will continue to explode.