It's a good thought, but until public transportation is a 1st party citizen in LA, this will just cause more problems in the long run. Busses are still seen as a method of transport for impoverished people, not for the masses. Trains and light rail simply aren't a priority for either the city nor the population. For comparison, Sydney is similar to LA in terms of density and affluence, but has 7.7 times as many people riding their rail transport[1]. LA should be focusing on creating a positive draw to public transport by increasing service, availability, and quality, rather than creating a negative pressure by decreasing parking availability.

[1] 359m annual ridership in Sydney with a 4.6m population, vs 108m annual ridership in LA with a 10.1m population.