I don't really buy this car-centric view. Don't get me wrong, I also like the idea of self-driving cars very much. But I don't think this will change "everything". Instead, I see a smooth transition towards more and more automated driving.
For example, here in Berlin we have a really good public transportation, which becomes more and more automated every year. In particular, short-distance (as well as long-distance) rails are almost fully automated these days, yet there is still a human sitting in the train's driver's cab for safety reasons.
In other cities like Frankfurt, there are even one or two non-human fully automated short-distance rails. Those are used more in the way we use an elevator, they feel less like trains.
Another example are airplanes, which are driven almost automatically these days, where the pilot is only really required for landing and, again, for safety in unexpected situations.
I think that cars are no different in that regard. There will always be some kind of "driver", although that person will have less and less to do with driving, and more with technical observation, safety, etc.
(As a side note, I think that putting so much emphasis on cars over other types of transportation is some kind of "US thingie". Here in Germany, cars are high valued vehicles, too, but they are generally not a symbol of freedom, independence, etc. Maybe I'm wrong in that regard, but that's my personal explaination of that strange car-centric view on transportation, which leads to so much excitement of self-driving cars, disregarding the amazing progresses in all other areas of transportation.)