LA doesn't have a traffic problem. People just have overly high expectations.
As someone who has also lived and commuted in lots of cities around the world, LA just doesn't have that much of a problem.
What other major city in the world would you expect to be able to drive 15 miles through the centre at rush hour and get to your destination in under an hour (I'm using as reference Downtown LA to Santa Monica at 9am, typically takes 35 to 1h 5min according to google maps). Good luck in London, Paris, NYC or Tokyo never mind Delhi or Beijing.
The line made famous by clueless that everywhere in LA takes 20 minutes is completely true, with the caveat being, so long as you don't drive during traffic. This reality is what people are comparing their rush hour commute to, they know that if they are lucky enough to avoid traffic they will get there in 20 minutes, but when they hit bad traffic it takes an hour. (Obviously I'm ignoring stuck on the 405 for 5 hour nightmare stories here, I'm just talking about day to day driving.)
LA is a victim of having too good a car infrastructure, it allows people to make ridiculous commuting decisions and get away with it the majority of the time. Adding more traffic infrastructure just makes the problem worse. People can drive from further away and save money on their housing and they will. They'll also work in places that are further away, the problem is as much about where businesses are located as it is about where people live.