In theory, this idea is great, but I think the number of car owners will not decrease as dramatically as some people think. But this number will shrink in densely populated urban areas where space is and will become really expensive. Letting the cars parked outside the city and only picking up the passengers will reduce the traffic in cities and increase the living standards.
I'm looking forward to the first mass-market ready autonomous vehicles even though the recent incidents with Tesla and Uber might push the date a little bit further into the future.