They only issue a certain amount of licences every year, no licence no alligator. As he said in the video the larger ones cause more harm to the younger alligators. Nothing is wasted, they eat what they catch.
It’s quite a strict system. The season is mid august to November and you have to apply for a permit and each permit allows you to kill two of them. Pretty sure you can’t hunt for them for more than a a week out of the first month or so of that period either or something weird like that. Permits area quite expensive, I think at least a couple hundred dollars for residents and over a grand for non residents. Think it’s cheaper if you already have a trapping licence (for land management or moving nuisance ones) but no idea how that works. State wide they grant about 7500 permits a year so only 15000 alligators out of a population of about 1.3m (human population is only 21.5m!) so it’s pretty sustainable. As Geoff says they eat most of them so it’s just like livestock really.