Seems like there's a simple solution here: Don't tie parking to housing.

Those that have cars and want to park them on the street should pay for a parking permit, then the local council builds parking spaces in line with how many permits they've given out. You're only allowed to park with a permit in your area.

Then those that really want a car can get one and find parking, and those that want micro apartments and don't need a car can have them too. Everyone wins. The prices for parking and the prices for housing are separated and both dictated by the market and it's fair for everyone.