If you look at an actual density map, LA is actually a lot denser than you give it credit for. There is no technical reason transit cannot get 40% of the population to work in a reasonable amount of time compared to driving. However in order to get there LA needs to invest in a lot more buses in dedicated lanes, and trains - both of which are not cheap. Don't forget to account for the overhead. In the long run it would be cheaper for everybody in LA if that investment was made, but in the short run a large investment is needed.

It doesn't help that transit costs 4x-7x as much to build in the US vs Spain. It also doesn't help that nobody cares about good investments - republicans hate transit and won't invest in anything if they can avoid it. Democrats love the idea of transit and waste a lot of money on slow, expensive lines to nowhere that nobody rides thus proving the republicans right that transit is a bad investment.