Think about the possibility of changing cars on demand. In the morning you can rent a mobile bed like car to get to work(take a nap while it takes you to work or get some tasks done), when coming home you can rent an suv to pick up groceries/pick up your kids and on the weekends if you need a pickup truck/van, you can request one of those for the occasion.
Yes there will be massive traffic implications. This is probably something that will have to be addressed when it happens. If there are dedicated self driving car lanes, can the cars communicate with each other to help reduce traffic? At the very least pollution will be significantly reduced from today's smog filled cities like LA thanks to the transition to EVs(I don't expect this revolution to occur before the transition to EVs).
Finally, in regards to public transportation: it is already a failure in the US outside a few cities. It is a lost cause in a society that focuses on individualism vs collectivism. In terms of walking/biking, I can see improved access to these services. Can you imagine how a car that never gets tired/drunk will reduce accident and subsequently insurance rates? If the cards are played right, there is an opportunity for a massive transformation of how bicyclists and public walkers are treated in relation to cars.