I like that idea. The links between each could double as public transportation for all, just include connections with existing metro stations. It would encourage the city to build around each of those nodes: put one in West LA, one DTLA, and one in the Valley, improve the one in Inglewood. The 405 from LAX to West LA and the 10 from West LA to DTLA are among two of the worst stretches in the country.
Though, people in for eg. West LA would have fits over the idea of airplanes flying over their sacred lands.