Personally, I hope it never happens. The US is still suffering from when its cities were redesigned for cars, vs. public transit and pedestrians.
Self-driving cars can and will play a very important role in transportation, but cities should be designed around people, not cars.
Edit: I'm by no means criticizing your hope, and I do agree with you that cities should be redesigned to "accommodate" self driving cars, such as "buffer garages" (where autonomous cars are parked in a FIFO way, not in the way cars are parked today), auto-charging stations, smart curbs for pick-up/drop-off, etc.
Taking the SF Bay area an example: Sure I can take the Caltrain or the Bart to get to nearly any city but it'll always be the long way around.
Think San Mateo to Union City. Crossing a bridge it's direct. The road infra structure is already there and the cities are built around it. Sure there's probably some cryptic bus route but the difference right now is (with a quick google) 35 mins vs 1.5 hr.
I think self driving cars have the potential to build on our car centric ecosystems. Look at how Uber/Lyft have adapted into Uber Pool and Lyft Line. They've done more to change people's driving habits than any changes to the public transportation system. I'm excited to see how self driving cars solve this by dropping the price point further and exploring larger pools.
that is the use case best suited for flying tub https://www.youtube.com/watch?v=EQK9m_OBVgY
But the problem is that car-centric systems are not scalable and sustainable.
Sure, self-driving cars would do well in the Bay Area, but they would only make traffic worse, as now people are willing to spend a longer time in traffic, since they are no longer driving.
Self-driving cars actually remove one of the negative feedback mechanisms of traffic.
What's so special about efficient routing with a driver-less car? There's no route that a human driver couldn't follow just as well if assisted by GPS software.
Putting people on a train is going to be far more efficient.
I think you are begging the question - are cars more dangerous than horses? Just from reading random history, it seems like a lot of famous people were killed by riding accidents. And even today when the vast majority of people don't ride horses, I bet you can name a famous person who had a terrible accident.