Why is there no Hollywood-Inglewood freeway?

I think we can all agree that for the most part, more freeways is not what LA needs, public transit is what's needed. But it kinda baffles me that there's no good North-South route in central LA.

Even freeway-locked neighborhoods like Huntington Park have logical freeway route choices to get to other places. But to go from Hollywood to Inglewood or LAX, what do you do 101-110-105, La Brea-10-405, 101-405, or most likely stick to the streets La Brea/La Cienega all the way down? There's the nice express stretch through Baldwin Hills, but it's still a painful route to drive and it's worse if you're somewhere in between like going from Ktown to Ladera since then you really have no other options.

What I imagine is a highway that roughly follows La Brea Ave connecting some of the densest parts of the city: Hollywood, La Brea, Miracle Mile, Mid City, West Adams, Crenshaw, Windsor Hills, Hyde Park

Here's two maps of what that looks like over the current highway system, and over the population density map (tho density can be misleading, since it makes it seem like commercial areas like Mid Wilshire are less important to connect) https://imgur.com/a/rzmrPTz