Japan's solution is to forbid owning a car if you can't prove you have a parking space for it (as a rented space or you own it, choice is yours).
It worked pretty well IMO, and car rental was cheap enough to cover the need to see grandma case.
BTW Paris is testing the casual car rental strategy also.
The fun part is, there is no strong definition of how much space you need to park a car, you have to prove you can actually park your car in the space you declare.
An officer follows you to your parking place, and stands there watching your maneuvers.
I don't think you have to prove that. In big cities like Tokyo and Osaka, most people use public transport to commute anyway. Although it's not mandatory, in practice every company will reimburse your commuting costs if you take public transportation.
BTW Paris is testing the casual car rental strategy also.