Those apartments would all cost more than 3k a month. Putting up high rises in LA is expensive. (Earthquakes, fires, etc). So there is zero motivation for developers to not get the maximum amount of rent possible for a given square footage.

No one has explained why a given developer should rent for less than 3K when they could easily rent the same space fo 4K? Is the government providing an incentive covering the shortfall?

Build enough housing & prices go down. It's worked everywhere it has been tried, and it'll work in LA, too.

This would shift the political dynamics in the rest of the US as people left for car-friendly cities where they could own their homes.

You can’t get to these areas without driving. Where will the residents park?