I think you shouldn't take Bear quite so seriously.
It's entertainment. No more. No less. If you're watching it as a serious exploration of survival skills then you're seriously missing the point. I enjoy watching Bear Grylls - it makes me laugh and is pure escapism. But I don't see it as part of the wider bushcraft agenda.
And so, when it comes to his 'killing' of animals, I don't earnestly believe these are animals he has trapped and killed in the manner he would have you believe. I am quite sure it is done in controlled conditions with supervisors on hand. And I am sure the animals that he kills are being lawfully killed for whatever reason.
Don't kid yourself that Bear does all these things 'for real' and you'll find him quite entertaining.