You don't have to register at the toilet with your ID/driver's license. You do however, have to do that when you use e.g car sharing, and the first question the system usually asks you, is: "is the car clean?". If no, then the previous renter will be liable. So this is already a solved problem.

If public toilets had a user reputation system (like Uber), they would be as lovely as the ones in Japan. Unless you had a bad reputation, in which case you deserve what you get.