Americans own cars because most of them live in single-family houses on large plots of land, and that doesn't make public transit for daily commuting a realistic possibility. In Paris car ownership is very low, maybe 1/3 of adults, but in rural France the car ownership rate is easily 95%+. I haven't seen a single developed area in the world that has violated the rule that low density = high car ownership and vice versa.
The other rule that I have never seen violated is that the large majority of middle and upper income people do not want to live near low income people, due to crime or other reasons. In Europe, poor people live in the suburbs, so the middle income live in the city with high density housing. In the US and some other places (south asia), low income people live near the business center, so the middle income live in low density housing in the suburbs. These are for historical reasons and cannot be easily changed.
I live in a large European metropolitan region with excellent public transport and bicycle infrastructure - at least comparatively. While both leave massive room for improvement a car is not needed, especially as alternatives like car sharing exist for moving heavy stuff once every few months.
There is quite the large support to completely prohibit car use in the inner city aside from transportation, taxis and deliveries. There are hundreds of streets and places where cars have NO value, take a lot of room, blockade other participants in public life and actively worsen the urban environment for everyone. Getting rid of personal cars in these areas would free up massive amounts of space as parking slots can be reutilized and 3-lane roads become single lane.
I love cars and love driving but I hate hate hate them in inner cities. Dense, well-connected urban centers are very suitable to completely outlaw cars whereas suburban or rural areas are absolutely unsuitable to do so.
An improvement doesn't have to be 100% on day 1.