The thing about Florida is that a lot of "lakes" are not really lakes in the sense that a lot of people think about them. They are old quarries or drainage systems for whole neighborhoods. Yes, they arn't natural by any stretch but they also usually arn't closed systems. From the outside they may look like a closed off lake but if you were able to look at it empty you'd see many tunnels connecting the lakes and canals into a massive network running from Lake Okeechobee to the Ocean or the Everglades.
If this is a closed off system then that'd be true, but if it is like a large portion of the lakes then no body ever had to bother stocking it.
And killing the fish is perfectly fine. They will keep breeding until they push out all competition then balance their own population. This isn't a good thing. Wiping out 21 might not put a huge dent in the population, but it also isn't creating an opening for the babies to fill. It is taking some of the stress off the native populations who have a lot of unfair competition on their hands. It is a losing battle but it doesn't hurt anything to do it either.
Down here I don't see as many Plecos but in some lakes I can catch Mayan Cichlids by the dozens without even trying. There is one lake nearby where because of the combination of Bluegill, Turtles, and Mayans bait doesn't last more then a couple seconds. Literally, bait hits the water and you are dragging in a 6-7" fish. Last time I tried to give any Mayans to a LFS they flat out told me the fish were considered worthless and they'd 'dispose' of them for me. They didn't even try to sell them.