It wouldn't be that personal vehicle ownership would be banned, it would just be drastically reduced. In its place there'd be far better public transportation options, maybe better fractional car usage options, bicycles rideshares, etc.

Many people would still need cars, but instead of every family needing two cars, many could just have one. Then even for the people with cars, they might not drive as many miles on average with the new options open to them.

Obviously it would be easier to reduce car ownership in denser areas so that's where the bulk of the shift would happen.