I'm not sure that anything you've said describes something resembling a solution, except in the very narrow circumstances of the sort of people who insist on living in cities where the cheapest apartments rent out for $4000+/month.
Yes, if the developers were allowed to come in and put up some high density something somewhere, those prices would ease back down under $3000/month (if only a little below), and the sort that's well into the six figures in six figure incomes would rejoice.
But we wouldn't see any difference anywhere else in the US (or, for those of you in other high cost of living countries, I dunno, London maybe?). No one living in Terra Haute, Indiana would be better off. No one in Boise, no one in Richmond, Virginia.
Nor is some nationwide laissez-faire policy going to do the trick. The flip-side of "housing costs too much" is "oh shit, the builders built way too much" and then the economy craters when that does more than just cool, but freezes over for a decade. If you wanted the blue collar folk to howl in agony, just wait til that happens. Or, just maybe, you think you have some special insight where you could perfectly regulate just how much construction occurs, so that there's no excess at all.
What if we've somehow gotten ourselves into a mess where there are no solutions at all? Like, mathematically. Like, if we had an extra century to work out the problem, we could prove there is no solution? What if there are too many people who need goods (homes, of course, but other things too), but who can't ever have viable livelihoods no matter how much low-quality education we stamp on their foreheads with C+ grades? What if UBI doesn't work, because in the part of the economy that is actually worthwhile, there's just not enough excess to tax away and send to them as welfare? What if we're still 150 years away from the technology that would give you your Star Trek post-scarcity utopia?
What would that look like? Could it look something like this? Like some really bad imbalances that, with a naive-enough outlook, seem as if they might still be re-balanced if someone were brave enough to make the hard decision?
A long time ago, before even some of you reading this comment were born (and for the rest, we were all still in school), someone decided that the United States was not going to make things anymore. We'd all be manicurists and day traders and lawyers and hip-hop recording artists. This is the result. Nor was it a good thing for places like China, where that's all they do, they're about to hit a wall too, and it's no longer clear Winnie can postpone that either. I don't think cannibalism will be widespread, but a few years from now you may wake up to realize that you haven't heard a dog barking for several summers at that point.