I grew up in a farmhouse, I've had pet mice and rats. My dad had a wild mouse he used to leave cornflakes out for. We had cats and dogs to keep the wild beasties hidden (they were terrible mousers). We've always relocated them when they were caught out in the open. We also relocated a bat from the living room ceiling fan to outside. lol
However, I had a dog who was "rat control", I don't mind the rats climbing in the feed bins, or even living in the basement, but once they attack my livestock (we'd lose chicks/ducklings all the time), or leave massive tunnels for me to twist my ankle in through the stall floors, then we have an issue.