Traffic jams are solved by congestion pricing. Parking lot congestion can be solved the same way with pay-parking lots. I don't know what cars have to do with "lost third places".
Congestion pricing works when there are alternatives. If you have both no public transport and congestion pricing, what you have is only increased tax collection with no behavioral change.
No, you'll get car sharing and even if just because you swing by a spot your friend recommended to pick up passengers to near you office, on days you feel like driving yourself, and likely become one such passenger yourself after a couple weeks of that, provided you're not amongst those who couldn't do it without their own car.
If you have to go to work to keep your job, then staying home isn't a great alternative. But there are others! Carpooling for example. Or, maybe you're one of the people that will keep driving. But not everyone is like you, and some won't.
A typical household would have 4-5 people in it and only two cars if you’re lucky. A person needs mobility from the age of roughly 7 to at least 70 for all kinds of reasons.
Please travel the Europe and see how they treat their people and how increased mobility creates a great environment and freedom for everyone. I assure you that it’s not a backwards place as some people claim.
As a side note: All this car craze coincided with baby boomers (roughly) and now that they’re losing their physical and cognitive abilities we’re seeing a lot more accessibility support from them (duh) and I wouldn’t be surprised if they started pushing for free public taxi service for themselves but nothing that would serve the public. And we’re not talking about heavily subsidized industries like cars, but something that can be profitable and worthwhile because it allows people to go to work, school, shopping, hospital, theater, and more.