New parkway regulations were first presented to Culver City council in May 2013. Transition Culver City has a great video up that explains exactly why curb cutting is so cool! Check it out.
Los Angeles building code has focused on getting stormwater off properties, into streets, then storm drains to the river and the Ocean. This is starting to change, and while curb-cuts are not visible city-wide yet, they are starting to popup around the city.