Every animal in the world has an impact on the environment, either positive or negative. In your example, if the alligator went extinct, fish populations would increase due to a lack of predation, causing a severe decrease in the population of the insects and algae that are eaten by the fish. One cannot say that an animal does nothing for the environment, simply because animals are part of the environment. At the very least, they maintain a balance between herbivores, plants, and carnivores.