Car based transportation is still needed for:
1. Shipping of goods/deliveries, etc....
2. Shipping of people (think elderly, sick, disabled, ambulances, taxis, etc..)
Best way to do this with blocks/chunks of the cities being pedestrian only, and roads with loading/unloading areas that come close enough.... but no parking, or maybe parking centralized underground in one place, with one clear entry exit (so people don't circle around to find parking).
Best solution I have seen is in Barcelona, where you have blocks cordoned off, and pedestrian only use, and still have streets that get close enough to these blocks... so you can do your deliveries as well....
Karlsruhe and Ulm in Germany do achieve this as well . (major areas are pedestrian only, allow cars to come close for loading/unloading, limited on-street parking, and parking in the center only allowed in some major underground place).
Most people can reach the center, if they really have to, but it discourages daily use of the car as it would be too expensive to park.