But I bought my cats specifically to do the job they were bred for, which is to catch vermin (rats and mice). They're cute pets as well, but that's not what we selectively bred cats to be.

The problem is that humans are invasive; stockpiling rubbish, building grain silos, and creating environments where rats and mice can hide and not be caught by natural predators.

If you live in a country where wildcats, or other larger predators, are indigenous, then I don't see the problem in letting them outside.