I have a screened in pool, the best reason to have one is to keep out the debris like leaves, pine needles, etc...makes cleaning a lot easier.
Growing up my parents had a pool without a screen, we did have the occasional rattlesnake get in the pool but no alligators.
If I ever move back, I may have to get one of those screened in cement ponds, but I can’t help it that I love living on the edge of water. So soothing. I think I would prefer the gulf if I could find a place that wasn’t so touristy. Gotta keep looking. Maybe I’ll find a needle in a haystack one of these days.