Cars are by now a hard to reverse environmental and urban planning disaster across the world. We are stuck with them. As a mode of transport it has grown uncontrollably at the expense of all others (except the airplane) and practically everything has been shaped to accomodate it.
Reversing that development, limiting car traffic to where its really needed is like trying to perform a complete heart and arteries transplant on a living person. Even if there was a will (which there is not) it is not clear if there is a way.
In the best scenario it will be an excruciatingly long transformation (~50 yr) as car oriented cities (or city sections) get slowly deprecated and the car-free or car-lite segments become more desirable, more livable.
The real problem is both cities that are not growing at all, and cities that are still digging into the car hole.
You might be able to rezone 50 year old suburbs, if just because the houses themselves keep losing value (as the real price increases are just land). But when the house was just built 10 years ago, it's a very tough sell. And if you expect a couple of million people, who are living in very low density suburb, to come downtown for any reason, you either make their transit story hell, or you are stuck wasting a lot of space just to manage their cars: Bad either way.
The cities that aren't growing just are going to have a lot of trouble becoming denser, and the political problem will be even bigger, as every effort to make the area near the city center denser in a city that doesn't grow is just making the outer suburbs less valuable. I am really worried about those cities. As having the infrastructure to support four times the number of people that you have is just a road to fiscal ruin.