The idea around reducing zoning requirements for parking is to allow a core to emerge. And everyone's agreed that it will take a long time. But it has to start somewhere, and it's more difficult if zoning requires (say) 1.5 parking spaces per 1-bdr apartment, even when in an area well served by mass transit.
You mentioned Santa Monica. Here's their planning commission report on parking for the city - http://www.smgov.net/departments/pcd/agendas/Planning-Commis... .
It includes: Reduce residential off-street parking requirements for some housing types in the Transit-Oriented and Mixed Use area to reflect actual Census data for household vehicle ownership and eliminate the visitor space requirement in all areas. Reduce off-street parking requirements for certain types of commercial uses (general office, hotels, restaurants, markets) in the Transit-Oriented and Mixed Use areas.
It also points out that while there is a "Perception of parking scarcity", that scarcity doesn't really exist. Indeed, "Santa Monica, like many other cities state and nationwide, has a parking supply that exceeds parking demand." Instead, "drivers will almost always choose an on-street space over an off-street space and indicates that the management of parking resources, not the supply, is the underlying issue."
Also... there's nothing that Eminent Domain can't fix. Ask the people whose homes were demolished to build the supergiant highways that LA is so fond of.
You have to get to work, and you want to do it quickly. The train is not going to do that unless you have a lot more of them going everywhere. People commute a long ways in LA and there is no thing as 'counter-commute.' LA has no central place. There is a downtown, but its just a place like any other.
LA is the very definition of a poorly planned city. But trying to horn it into a planned city will take many many years. You have tons of issues to deal with. You might be able to encourage a planned city, ala this metro line seeding growth in the right places. However, it is just going to take a long time.