I volunteer at a Florida SP. I can tell you that the Campground is the park's biggest revenue generator. So, I am in favor of the state expanding its campgrounds. They would easily pay for themselves. Financially, Florida state parks are in better shape than most states.
That said, the reality is that public space in the Keys is very limited. The state has no obligation to provide campsitesin a particular region. Deal with it. It would be possible, however, to enact length of stay rules that only apply to specific parks. I think, a maximum of 14 days within a calendar year would be fair. Of course, if you did that, some people would reserve under other names, which would be a rules violation.
Reserve America could also defeat bots, but they don't really have any incentive to do that.