We seem to have plenty of hunters, thanks. There are much bigger threats to public safety in this state than the alligator population. As with most wildlife, human development still poses a greater risk to them. Most incidents of nuisance alligators are caused by fools who decide to feed gators who happen to live near populated areas. Then the gators, of course, start to expect food, pets disappear, and the nuisance gators are removed/disposed.
I frankly have never noticed whether there were gator warning signs at WDW -- because I don't have little ones to worry about and I live here so I know what lives in the water. Given the rarity of these events and the great efforts Disney seems to take to control the population and remove larger/nuisance animals I can understand why they decided not to post gator warning signs.
The large wildlife preserve near my home has explicit signs stating "AT DUSK, IF IT MOVES IT'S FOOD" with silhouettes of a large gator, a raccoon, a bunny, and a child. Graphic, but seems to get the point across.
My heart breaks for this family.