Many countries have usable public transport (buses, trains, metro, trams, taxis). London already imposes a punitive levy on private cars within the city, the result is a slight reduction in car traffic and no appreciable effect on shopping or pedestrian traffic. It would be very interesting to find out what a complete ban, or a much higher levy, would do to the city, but I doubt very much it would kill it. Do you have an example not in the us where this has been tried?

As long as there are other ways to get around, a city does not need cars, in fact cars are a negative for most denizens.