One thing I'd like to point out, although the smell of cats, specifically their pee, normally does scare off mice, if the mouse (or rat) is infected by toxoplasmosis it will actually be attracted to the smell of cat pee. Also cats are much more effective at deterring mice if they are indoor/outdoor, that way the smell of the cat is not just in the house but also a lot of cats will potty outside and mark territory around the property.
As others have said hunting is part instinctual part learned. So unless your cats where taught to hunt they may not understand hunting past just playing with it like a toy. A mouse or rat will bite and scratch, so that can turn a cat off wanting to play with that kind of "toy". I know with my cats when I add a new cat to the house they will actually teach the new cat to hunt. They even taught my dogs to hunt mice when they were pups too. So maybe you need a proven mouser to teach your other cats what to do with a rodent? hehe
As others have said hunting is part instinctual part learned. So unless your cats where taught to hunt they may not understand hunting past just playing with it like a toy. A mouse or rat will bite and scratch, so that can turn a cat off wanting to play with that kind of "toy". I know with my cats when I add a new cat to the house they will actually teach the new cat to hunt. They even taught my dogs to hunt mice when they were pups too. So maybe you need a proven mouser to teach your other cats what to do with a rodent? hehe