To see a possible outcome of restricting the availability of parking, look at modern-day Russia. The streets and parking there were designed for a very small number of cars, since most people were expected to use transit. Then public transit failed, and cars became affordable for a lot of people. But there is still no parking, so people must not use cars, right? No, now there are major traffic jams and problems with illegal parking in every city.
There has to be a viable alternative to cars (good public transit, walkable cities).