Because no one eats live animals really, for a good chunk of animals eating them raw is actually dangerous and you can get very sick. Very few animals can be safely consumed when alive.
Other animals have different digestion systems and thus why they thrive on live or raw meat. I also think most live animals would resist trying to be eaten, if you have a wolf let's say fully alive and you put him on a plate the second you try to cut into the meat he would freak out and fight back. Even in the world of animals, they usually kill the animal before eating it.