I've written a lot about the problems inherent in government-mandated parking minimums: structured parking is incredibly expensive, and takes up space that could be used for more housing and other productive space; minimum parking requirements produce more parking than necessary, encourage more driving, usually result in pretty ugly buildings (anyone else sick of parking podiums yet?), limit opportunities for redevelopment and reuse of aging buildings, and end up forcing non-drivers to partially subsidize parking spots for car owners. On top of all that, developers already have plenty of incentive to build enough parking: if they build less than residents want, they won't be able to rent or sell their units.
All that said, parking mandates do provide some benefits to incumbent residents, even if it's at the expense of future residents. In moderately dense neighborhoods, on-street parking tends to be highly sought after and in short supply, and forcing developers to (over)build structured parking limits the amount of cars that spill over onto the streets as new residents move in. It's not a fair system, since the streets belong to everyone (theoretically), but it's easy to understand why residents often support these kinds of rules for their own narrow benefit.
But what about places like Downtown Los Angeles, where there's basically no long-term on-street parking whatsoever? Downtown is less than six square miles and has a population of around 50,000 people, a number that balloons to over 200,000 on weekdays during work hours. Even if you provided on-street parking along every inch of curb you couldn't make a dent in overall demand. Unlike in less dense parts of the city, there's nowhere for cars to spill over to if there's not enough structured parking for them. Developers are aware of this, and if they want to attract people with cars, as many of them obviously do, they're going to provide parking whether you force them to or not. Parking minimums aren't benefiting anyone in Downtown LA, but they're almost certainly creating an oversupply of residential and commercial parking, and they often force those that don't own cars to subsidize parking spaces for those that do.
At this point, Downtown parking minimums are a solution in search of a problem. The same is true in many dense neighborhoods across the country: when the number of cars outstrips the number of on-street parking spaces by orders of magnitude, parking mandates have outlived their usefulness.
I don't support parking minimums in any city or neighborhood, but I don't expect to convince everyone to agree with me on that point. It should be obvious, though, that the narrow benefits of parking minimums simply don't apply to a place like Downtown. No matter how you feel about cities, public transportation, or anything else, I think this is something we should all be able to agree on. Parking minimums may have served some purpose back when Downtown was less populated, but their time has passed and it's time for them to go.