If you build housing with no parking attached to it, you won't be able to sell it for as much money. If people really care a lot about parking, that housing will have to be a lot cheaper to attract buyers. Perhaps so cheap that the developers won't make a profit on it and no one will build that kind of housing.
As elsewhere "what is the correct amount of parking for a given unit of housing" is basically impossible to solve at a citywide level and is a perfect example of this, posted elsewhere: https://en.wikipedia.org/wiki/Economic_calculation_problem
Most likely there are different kinds of people - some who care a lot about parking, and others who ride their bikes all the time or something. By providing diverse amounts of parking, people will sort out into different places that most suit their needs.
Maybe bathrooms should be optional? Some people may prefer to shit out the window or use the local YMCA to shower? Yeah that's a sanitation concern, but parking is a transit concern, both are major issues in cities.
There needs to be some forethought into how the new residents are going to get into and out of the city. Simply leaving it up to profit seeking businesses to sort out doesn't mean a functional solution will actually be found.
Build your city in a grid, and adapt. 150 years ago, that forethought would have created good infrastructure for horses. Now, that might not be so much of a concern. As much as possible, people should be free to choose. See also: The High Cost of Free Parking: http://amzn.to/2dRbceN
The other answer is that if you're asking me to weigh a place for someone to live against someone else's privileged ability to conveniently have everyone else pay for them to park a car, I'm going to favor living space every time. I think cities favor cars too strongly.
Every time you mandate parking spaces in new developments, you mandate the continuation of the car-centric city model that is simply unsustainable once the population grows past a certain point. Cars are effectively being subsidized by the government in most cities. That money should be spend on transit instead.
Serious rail projects take on the order of 30 years. I think it's much more likely that people would go somewhere else, rather than endure an entire adult life without acceptable transportation options so that maybe the grandchildren would have it better.
They sure as hell don't take 30 years when they care, though. How long was it to get 405 expanded with another lane? And for all that it's now even slower than before!