[alt text: an illustration of a person with a head-empty expression on their face, who is saying, "Not letting your cat outside is CRUEL!" Around the person are various gruesome scenes of different cats in distress. From the top and going clockwise, the scenes include: a cat being carried away by a hawk; a cat that is on fire; a dead cat in the road that has been run over by a car; several dead kittens; a cat that is missing an eye and various patches of fur; a cat that is feasting on a songbird; and a cat that is being carried away by a coyote. The person appears to be completely oblivious to these scenes of distress.]
There are native mice all over the place. Yes, some are introduced/invasive, but there are also plenty of native ones too. If you live in the Americas, here's the subfamilies they make up:
https://en.m.wikipedia.org/wiki/New_World_rats_and_mice
Mice serve as food for animals like owls, hawks, falcons, snakes, skunks, etc. Cats killing these animals' prey makes it harder for them to find food.
Didn't know that "owls, hawks, falcons, snakes, skunks, etc." all live inside of buildings.