If the market determined the price of parking then people would flip out because parking was only affordable to the middle class and it would instantly be framed as an anti-poor thing.
Car ownership is lower among people with very low incomes, but if they want a place to live they still have to pay for parking to be built. Shoup’s book has some examples of proposed low-income housing that ended up getting blocked over parking minimums, even though most of the would-be residents did not own cars.