We spend the winter in Florida and southern Georgia staying at state and national parks for varying amounts of time. Out of curiosity this winter, I've been checking the license plates in each park, and in every case the predominate plate has been from Florida. The one exception is the Georgia state park just over the Florida line we're in right now where there's currently a fairly quick site turnover as snowbirds head north. But even then, it's a toss up between Florida and Georgia plates at the longer stay sites.
If Florida didn't want to us to move from state park to state park, I'd think they would institute a minimum "time out" between booking into any state park, rather than just re-booking into the same park.