Plenty of people in cities get by on taxis and car-share, self driving cars will expand that to suburban areas.
Plenty of people in cities get by on public transport, and it's generally quicker in a lot of major cities.
Sure public transit is good for everyday trips, but still it's nice to have access to a car (even within the city) to take you point-to-point instead of waiting on transit and possibly adding blocks of walking to your journey. Things like getting taking your date cross-town from a restaurant to her friend's party on a rainy night, taking the dog to the vet when he injured his food and can't walk, going on a weekend camping trip out of town, etc.
These are the times when it's nice to have access to a car, but you don't neccessarily need your own car - take Uber or a taxi when you're in town, use carshare or a car rental company when you want to get out of town - take the car-share 4WD SUV when you're going camping, take the convertible when you're driving down the coast to a B&B with your partner, rent a minivan when you're taking the family for a week long road trip. When you don't have to own a car, you have a lot more flexibility in what kind of car you get when you *do* need one.