I don't approve of any animal being hunted for food when it is unnecessary, but killing the predators is especially tenuous. Those predators are regularly killed by ranchers and others who perceive them to be a threat to livestock or their families.
Most predators already exist at dangerously low levels.
And I'm sure you know what problems this causes. If you are established in one place, you can grow your own food. Something to consider. BTW, I admire your interest in a life of that sort.