Even in a city with good public transport, you sometimes need to drive. But cities should only have city-appropriate vehicles: Cars limited to 35km/h, small and light, electric (for noise and air quality issues, and because 'range' isn't an issue for city driving). Some would be big, like delivery vans or workman's vans, but most would be mini-sized.
Also, let's bring back city walls.
The only practical issue there would be, people getting their legacy/distance car out of the city center to the highways outside the city wall. I guess you could have garages and rental companies at the walls where people either swap between their city car and legacy/distance car or rent one.