Or just do what the Japanese do - remove unlimited (and overnight) on-street parking in urban areas and require anyone owning a car to prove they have a private parking spot to house it
That would be a good idea, but one of the main impediments is the fact that heavy regulations make underground concrete structures (and hence underground parking lots) very expensive, a lot more than in Europe or Asia, where it's often economical for even 3-5 story residential buildings to have underground parking space. That's the reason why developers push for on-street parking.
That's pretty drastic, and would probably only be the best alternative on a densely packed island. Seems like overkill for any other situation.
I think you're also forgetting the other aspect that allows this which is having readily available public transport.