Minimum parking requirements are a big deal for low-rises, where the parking area is an appreciable portion of the building's overall square feet.
The gleaming 40+ story high-rises in the Civic Center/Van Ness area run from around $3000 to $5500 for a basic studio or 1-bedroom. There are also several parking garages in the area, distinct from the residential buildings, where a monthly reserved parking space is around $375.
Assuming parking is built into rent (it isn't) and a 1:1 ratio of parking spaces to apartments (it's actually less), removing minimum parking could only bring the rent down by $375.
I think the real explanation is that desks are much smaller than apartments. Approximately everyone at Twitter, Square, Uber, etc. is willing to pay a substantial portion of their six-figure salary for a trivial walking commute. To have a corresponding apartment in the neighborhood for every desk at Twitter, Square, Uber, etc. would require dozens of residential towers. So when only 3 or 4 are going to exist, they have to priced to skim off only the very top of the corporate ladder at those companies.