Indeed, in the US you insure the car, since the scenario that someone may have to drive it is common. That said, the insurance tends to recognise risk in similar ways, so more expensive for younger drivers, etc.
The only thing that made us get rid of a car was the awkwardness of parking when we lived in Shepherd's Bush, it just wasn't worth the hassle to end up parking three streets away after fifteen minutes circling the area. And it did raise the question, why the hell do so many people in zone 2 need a car. Owners seem to accept costs, which is I assume why they sit there with the engine running.
Ultimately, if you want to discourage car use, you have to make it less convenient (while at the same time making the alternatives more convenient). Taxation may address some of that, but of course, the burden falls disproportionately.
Possibly the ultimate problem is that we've spent a lot of time and effort in building a society where we have to drive everywhere, often without an alternative. That's something we have actively encouraged in numerous ways but which we don't benefit from.