I'm not doing what you describe (we rent a specific site) but I believe there are places like that and we may have members that are doing as you describe.
Think about where you want to be; population density, availability of conveniences (Walmart, shops, auto repair etc.), type of "population" you will be surrounded with and of course costs vs what's offered. There is a huge difference as you go further S in FL and even between the L and R coasts. The Gulf is different from the Atlantic. Tourist meccas such as Orlando, Miami, Ft. Lauderdale, Key West etc. have crowds and "different" kinds of folks vs rural areas. We like simple, rural and quiet.
I do know of one place in this area, Wildwood Golf and RV resort, that used to sell their sites. When I visited with them a few years back, you purchased the site and used it when you wanted. When you left they would rent it for you then split whatever was brought in. Seems the split was 60/40 (IIRC from aged memory) and don't remember which way the split went. At that time IMO the best sites had already been purchased so we just rented by the month.
Good luck in finding a spot. It really is nice here and sure beats cold weather and snow!