While I've never been there, my impression of LA is that it's very sprawling. Maybe not everyone has to go to one central area to work. Unlike Chicago's Loop or lower Manhattan where a lot of the commutes tend to converge in one general area. If few people have the same commute destination, individual cars would be more effective than mass transit.
That problem is already solved, and it doesn't require light rail: Privately run shuttles and busses.
It'll never happen, as it's opposed by (1) Taxi operators, (2) Mass transit operators & unions, AND (3) Do-gooders who don't want private business to succeed where public service has failed.