In the absence of predators, the natural tendency of any animal species is for the population to explode from high breeding rates. The critters then destroy the environment as they try to hold off starvation by eating everything in sight. You need predators to keep their population in check
Four-legged predators have their own problems. Deer make annoying neighbors in suburban developments (as they eat peoples perrenials, rosebushes, tomato plants, and whatever else they can think of) but controlling their numbers by introducing wolves and mountain lions creates problems for any people living nearby (as those California bike-riders discovered). Little kids make tasty snacks for predators who have lost their fear of man (They only DEVELOPED a healthy fear when being seen by a human meant you were going to get shot)
The only predator capable of holding down animal populations without creating worse problems for people, are human hunters and trappers. License fees from hunting permits also pay a lot of the expenses associated with keeping the wildlife preserves and parks open (camera-toting bunny huggers get in for free)