Don't leave cats like this outside. It's not okay for them to kill wildlife.
If not, why you think it's okay to condemn another living creature to such a life sentence? After all, its well-being is just as important as yours, is it not so?
Cats seem pretty alright with "lifetime seclusion", anyways. As with other domesticated pets, the only reason they exist is because they are, on the whole, happy being domesticated; if they all hated their lives (in a way that we were aware of), we wouldn't breed them to begin with.