Yes car is king in LA. In recent years though Lyft/Uber have changed the game a lot. I'd say it's cost effective to not have a car at this stage, especially when you add in the cost of parking.
It depends on what you mean by LA. LA itself actually has fairly decent public transit (by US standards, not NYC, but by nearly every other city) -- the RapidBus busses are actually fairly rapid (they can control stoplights so they always hit green) and the Metro is quite nice where it goes.
I'd rather be anywhere in Seattle or Portland trying to use mass transit rather than in LA, its so spread out due to zoning (requiring abundant, unused parking, and limiting building height) and all of my past experiences there have been piss poor with mass transit in LA. San Diego is slightly better, but it has the same issue as LA with zoning.
I do not think I could reliably take the bus to work in LA or San Diego, whereas in Seattle or Portland I grew up riding it and I know I'll get there reliably.
Interesting that you mention San Diego. I used to live there and actually took the bus to work. But I'd say mass transit is actually better in LA (which I would use while visiting) than SD. In San Diego, busses came generally only once an hour and most stopped running after 7:30pm making it impossible to use them to go somewhere after work. LA buses generally ran all day and every 15-30 minutes. which made them much more convenient.
If it runs less often than every 15 minutes, then its not a major bus line, and your in a suburban slum. Or, possibly your local transit agency has decided lifeline service to the suburban slums/gricklegrass is more important than urban transit, in which case its time to get the management canned.
Serving suburban slums with mass transit will never provide effective transit, nor is it financially feasible for most of these areas to maintain their infrastructure long term, usually they are underwater 5x to 6x in terms of maintenance funds needed to keep the current level of infrastructure afloat.
Richer areas may be able to make it work past the 50 year mark for a few decades more, but poorer areas (Detroit, Flint, and good chunks of Texas) are literally letting their infrastructure fall to bits as the tax base can't support it.
San Diego itself (where I lived, near UCSD) is a "suburban slum" in terms of density. I now live in an actual suburb of Washington DC and it is far more dense than San Diego (as well as being on both the DC Metro and commuter rail lines)