Part of the solution might be using the local population density to inform how much of the street you devote to cars. For example, in rural areas, two lane blacktop with no shoulder and 100% devoted to cars is ok, because there aren't many cars, so people can still use the road even if they aren't driving. In the suburbs, car travel lanes should begin to narrow, sidewalks should appear, bike lanes should appear, etc. In the densest part of the city, the streets should give space to transit, delivery/infrastructure vehicles, low speed transport like bikes, scooters, etc. and people. Primarily people and transit

Ideally there would be expensive parking lots right at the edge of the area, and cheaper parking lots further out. So you could park and walk right at the boundary, or park near the Broad Street Line and take that in. Or you could park at a Regional Rail stop even further out and take the train all the way in. Or you could Uber right to the boundary. Depending on where exactly you live and how much you value time vs. money, different options will make sense for different people. But considering that the people who will be getting dropped off right at the boundary would have otherwise been driving to the city center, it doesn't make traffic any worse.

The car-free zone makes sense if it's smaller than the area that has public transit. Note that even in the complete absence of public transit, you can still comfortably implement about a quarter-mile radius of car-free area, since a quarter mile walk is only 5 minutes.

In the US what we're mostly talking about is closing individual downtown streets to through traffic (like, say, Market between 5th to 13th, ignoring the City Hall death circle). On NYC 14th street, any car is allowed, as long as it turns off within 2 blocks. This greatly limits the usefulness of the street to through traffic, (and therefore makes it a much better pedestrian and bus environment) without changing the parking situation at all.