We have strict management of deer on our club. If you shoot something that isn't legal by the rules, break out the checkbook, it's going to cost you.
Hogs are a nuisance, the standing rule is kill every one you see. They are prolific breeders and can multiply many times over in a year. They destroy habitat and eat food sources before deer ever get a chance. But, they aren't stupid either, daytime activity goes way down as a season progresses.
Alligators are becoming a nuisance as well. I live in a neighborhood on a golf course and we have them in the ponds of the course. They are getting bolder and more aggressive towards people as their natural shyness wears off due to more encounters with people. I for one would hate to see a child or someone's dog get snatched by a 8-10 or bigger gator. Though they do make desirable shoes, wallets and purses.
Coyotes, foxes and bobcats are major predators on fawns, rabbits, quail and turkey and have to be controlled in order to keep the game species populations up.
What you perceive as indiscriminate killing of some animals is sometimes merely population and predator control in order to facilitate the advancement of the game species we pursue.
Thank you for the concern for American animals, now, go worry about those in your own country.