That isn't really how I see it ending up.
I think it is more likely that people will lease access to a self drive network of vehicles. These vehicles would be centrally maintained and their locations and pathing would be planned in such a way that you never had more than a couple of minutes wait time for one to pull up.
Currently cars spend most of their time stationary. If you can increase their utilization then you would have massive efficiency gains.
Special cases like baby seats and the like will have to be solved some other way. Potentially we would see almost zero crashes in the future which means those seats may no longer be necessary. But that is going to be a long way away.