I agree that roads are public infrastructure, but car owners are heavily taxed in Europe, especially some parts of Europe.
In Italy, excluding fuel taxes (which cover 70% of the cost of the fuel BTW) every car owner pays a mandatory "car owning tax" for each car they own, that totals around 5-6 billions euros/year. And it's only the main one, there are several others.
Forgetting fuel taxes?
Take the neighborhood I live in for example, It's all one-directional traffic with tight corners and speed bumps. It has more exiting streets than entering streets. The end result being a decided lack of traffic, while still being able to get a car to your front door when you need it.
Kids can play in the streets safely enough, There's a couple cars an hour most of the day and the few cars that do pass are going slow enough to not hit any kids. The most dangerous time of day is all the parents getting their kid out of school by car.
You sometimes see a commercial vehicle trying out a new shortcut. People only think that to be a good idea once. Going around is faster than going through in any case.
Carless doesn't have to be an absolute. It's a gradient from six lane highways through your neighborhood on one side, and no cars at all on the other. A balance needs to be found.
The same complaints playbook every time in every city (commerce, disabled, deliveries and repairs) with the same success stories each and very time the carfree streets and regions are there.
Rents are skyrocketing in Berlin because everybody and their friend wants to visit us or live here. At the same time for decades no new buildings were built. Remember? Supply and demand.
Yet rents are still not as high as in New York, London, Paris, Munich or even Hamburg so that people from everywhere flock here.
Oh, and of course being comparable in speed to at least a bike.
That leaves only subways...