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.
Prioritize dense, mixed-use development within ~.5 miles of transit hubs. Every new subway/light-rail station should include rezoning with a focus on a livable mix of commercial, residential, and retail.
Remove parking minimums. Let the market determine how much parking is available and how much it costs. Plentiful, free parking is not a right.
Remove single-family zoning (allow accessory dwelling units and duplexes in existing SFH zones).
None of this will work overnight. It will take years. But, the basic goal is to make living near work achievable and desirable.
And how do you suppose LA does that? LA isn't a centralized city. Relatively little of it's business and traffic is going to DTLA specifically. People are going to Pasadena, Santa Monica, Culver City, Encino, Sherman Oaks, West Hollywood, etc and they're all coming from various places (SGV, South LA, the Valley). All higher density development would do is exacerbate the issue, we need the public infrastructure to catch up so it can handle higher densities.