A future with self-driving cars makes more sense if all cars are taxis (of some form). Why leave your car stationary overnight (except perhaps to charge) when it can be out driving people around and earning money?
I'd like to see a system where one could purchase a guarantee that you'd get a car of a particular class to take you where you need to go within a given time (shorter time, higher cost; if you decide you can always wait 60mins for a ride from the time of booking the management of availability is far easier). Or, you'd just book journeys in advance - cheaper if you match logistical requirements. Then car ownership can be far more optimally managed.