This is the approach Singapore (and in some ways, Hong Kong) takes; you can own a car, but you must purchase a 10-year use permit, which costs in some cases much more than a car itself (something like $80,000 over 10 years). So if you're buying a Toyota Corolla ($20K car), you'd still need a $80K operating permit to use it.

That's why 90%+ of the people in Singapore use public transportation or carpool. Granted, you would need the public infrastructure for that to be possible. But if you make cars unaffordable for the average person, suddenly there would be A LOT more pressure on local government to get public infrastructure done.