We must first remember that all cities were car-free little more than a century ago. Not all cities responded to the advent of automobiles with the same enthusiasm as the cities of the United States.
In fact, some cities never did adopt the car. Venice was unwilling to destroy itself in order to build streets wide enough for cars, and therefore has never had them except in a sliver near the mainland.
The same situation exists in the Medina of Fez, Morocco, and several other North African cities. These districts are usually the most vibrant parts of their cities.
Cars were never necessary in cities, and in many respects they worked against the fundamental purpose of cities: to bring many people together in a space where social, cultural and economic synergies could develop.
Because cars require so much space for movement and parking, they work against this objective — they cause cities to expand in order to provide the land cars need.
Removing cars from cities would help to improve the quality of urban life.