Edward, Gator and chicken farmers have been experimenting with your idea. I met one in East Texas who was taking downer chickens and feeding them to his alligators, which are of course, immune to bacteria from rotted meat. The U.S. Fish & Wildlife and the U.S.D.A. goons had a fit. By federal law, dead chickens must be disposed of in a presribed manner and feeding gators is not an option.
And as far as killing the OLD alligators, the state governments in Louisiana, Texas and elsewhere are complicit---they share the blame for not exempting them from the legalized hunting. I understand the point about making a living. If being poor and working hard is an excuse, then I have more sympathy for marijuana farmers.