I feel that if you own the land you should have free reign to do what you want on that land. Including killing any animals on your property that you find to be either a problem or just plain tasty.
Nope. Maybe coyotes and other pests, but not game animals. And, yes, I do own land with plenty of turkeys and deer, but we leave them alone unless we have a license for them. The game licensing system works pretty well, let's just leave it alone.

Also, I have a cousin who is a rancher. He doesn't make "a lot of money" on anything, but he manages his resources so he can make a living off the land. Wheat, hay, cattle and hunting (he's an outfitter too). You need to use all the resources of your land to make it pay, especially with what land costs these days. You just have to hope that a bad wheat crop will be offset by a decent price for beef, or vice versa.