People will talk about induced demand and all that. But those people really just want to be able to get around. The fact that they just don’t because the traffic is so bad doesn’t mean you shouldn’t add more lanes. It means you should add a lot more. Same with the one lane at a time approach. The fact that it didn’t work does mean you are doing something wrong, but it maybe that you need to add 5 lanes at a time, not one. Now I’m not saying they should actually do that, just that the arguments against are BS.
A comprehensive public transit system, well maintained and well patrolled is what LA really needs. I am talking Paris metro on steroids. And it is going to cost in the trillions. But it isn’t getting any cheaper by waiting.

There are other reasons.

Adding, say, a sixth lane doesn’t increase capacity as much as adding a 2nd lane, because traffic jams are generally because of interactions. It’s very rarely the straight road that has a capacity problem. Adding a sixth lane adds capacity, but also creates more interactions.

Also, car lanes have a shit capacity, which goes down massively when it’s busy. Like you said, mass transit is vastly superior, but even a dedicated bus lane would help. In contested traffic, a car lane transports less than a single bus per hour.