Predation is the natural order of things.  Creatures prey on cats, too.  And yet, we still have ample numbers of both birds AND cats.  Whatever did we do before cats were allowed indoors?  And were allowed to keep their claws?

I had a cat that was a prolific hunter, even though he had been declawed.  It's true that some cats are just meant to be hunters, and some aren't.  The three I have now watch squirrels walk by.