Sure people will buy self-driving cars. People want to own things for themself. If a car has a higher value with this feature even more people want to have a car. Consumers don't think economically.
I'm skeptical about the "no one will own" meme. That said, there's no reason cleaning would be any more of an issue than it is with Zipcar today. If you go to pickup a car and it needs cleaning, you refuse it and report the problem.
Then what? What if you have something pressing to get to? All these rideshare arguments fall flat on their face when it is anything other than "going out" without much of a timeline.
Ever call a taxi (not in city) ? 30+ minutes.
Also, tragedy of the commons ... who was the last one to use the car has to pay for clean up.
How to accomplish that ? ... "No the other guy did it ..."