Via Alex Block, your obvious-but-important research finding of the day is that when you liberalize parking requirements people build more dwellings and fewer parking spaces. That's Michael Manville "Parking Requirements as a Barrier to Housing Development: Regulation and Reform in Los Angeles":
Abstract: Using a partial deregulation of residential parking in downtown Los Angeles, I examine the impact of minimum parking requirements on housing development. I find that when parking requirements are removed, developers provide more housing and less parking, and also that developers provide different types of housing: housing in older buildings, in previously disinvested areas, and housing marketed toward non-drivers. This latter category of housing tends to sell for less than housing with parking spaces. The research also highlights the importance of removing not just quantity mandates but locational mandates as well. Developers in dense inner cities are often willing to provide parking, but ordinances that require parking to be on the same site as housing can be prohibitively expensive.
Something to note here is that it's not that developers didn't provide any parking. It just wasn't always as plentiful or as directly proximate as it otherwise would have been. The inflexibility of proximity rules is a fascinating issue in its own right as seen in the sad case of the would-be Anacostia Playhouse. The idea was to repurpose an old warehouse in a largely blighted area as a theater, and have some parking spaces in a lot across the alley. But the zoning code as written requires the parking to be on the very same lot as the theater, which can't be done in this case since there's already a building on it. DC normally tries to handle this kind of unreasonableness through a time-consuming variance application process that gives sundry NIMBYs and extortionists different opportunities to hold people up.
Common sense says that the theater operator is well-aware that many patrons will want to drive to his theater and is capable of coming up with a reasonable solution that accounts for the local geography on his own. Who cares that the parking facility on the other side of the alley isn't technically on the same lot? It's irrelevant in practice, but it makes all the difference in the world to the zoning code.