These people would never afford whatever becomes available in an open market anyways. Cut the prices a bit and it'll be me moving to LA and I can outbid anyone living in a car out of necessity.
So, we're left with trying to make constant concessions just because people were born here (well, maybe) or we can cut them loose until they move.
If I can grow up in the Midwest and move away from home (nearly all of my hometown friends too) to progress my career, people can pack it up to progress their lives. There was no government intervention to keep families and friends together in the Midwest. Probably because we weren't addicted to Ohio.
People born in LA that can't make it either squandered a huge head start being born and local to LA or their family screwed them by staying in a bad situation and should have moved decades ago. What is so sacred about being born there? Their local friends/family are letting them live out of a car or a tent. What love will be lost?
They can't afford to live where they were born. Deal with it. It's over. Grind out a year or two in the heartland and move back with a better job if you really miss it that much. I don't think that's too tough of a pill to swallow.