In Japan you have to vouch that you have a parking space for your car. I think a similar rule would work for the states. However, it will cause a huge tension between the parking spot haves and parking spot have nots, without adequate equality will be seen (rightfully so) as a move to limit cars among those who can't afford parking spots for them.

For better or worse, the USA has basically made a contract with its people that "you have the right to a car, and because of that, we will provide really sucky public transit." That contract has to change before we start aggressively taking cars out of the system.