Dogs poop in the house sometimes too. Anything living will poop in your house if you let it in for long enough. It's nice they are considerate enough to go in a box and not in the floor

But human poop is perfectly fine? You saw that one Mythbusters episode, right? Feces is everywhere.

Cat flap in a door solves this, but you do need a vented room to keep their litter box that's not a garage because those usually need a fire rated door.

Air purifier are useful tools for a lot of things.

Cats poop outside.

They just don't need a chaperone to do so.