Yes, let’s ask the mountain lions and jaguars in Texas how well that worked out. Or timber wolves, grizzly bears, black bears, and others in much of their historical native ranges.
There’s a reason the scariest thing in the UK is a hedgehog. lol They hunted everything else into extinction. Just because you have the
right to do something does not make it the
right thing to do. People once thought the oceans were too vast for us to affect them. We now know that is wrong.
That being said, if your animals are properly contained and protected from predation, and you experience losses, I think you are within your rights to remove a nuisance animal through humane practices. But
your rights, just because you have the mental capacity to think of them, does not mean animals doing what comes naturally to them is any less important or rightful.