I don't think cars can be completely eliminated from cities, but I'm reasonably sure that we can remove at least 2/3rds of the car traffic by a combination of better urban planning, and better public transport. I don't think you have to restrict yourself to walkable distances. Ten minutes on a bike allows you to go several kilometers. I bet I can reach a quarter of my city in less than 15 minutes. If we make cycling safe and comfortable, that alone can eliminate a lot of traffic. Add in good public transport for trips that are longer than a few kilometers, and another big chunk of car traffic becomes unnecessary.

I lived a few months in Tokyo, without a car of course, and got by very well with a shitty mamachari and the subway. I wonder what the modal split in Tokyo is like, compared to other cities. I bet most person kilometers are met by trains and subways.