You're mistaken about the reasons why solutions are unpopular. Have you actually talked to the most active NIMBYs who oppose new housing development? Most of them are barely aware of affordability and home prices. They have lived in the same neighborhood for decades and intend so stay there until they die so prices don't impact them at all. Instead they are concerned about quality of life issues: traffic, parking, noise, petty crime.
My point isn't about the most active NIMBYs; it's about the central mass of the voting public. Yes, the NIMBYs have disproportionate influence, but politicians still have to keep their voters happy.
Perhaps my view is too California-brained, but homeowners here like high prices because it gives more flexibility to downsell, they can get large home equity loans, and Prop 13 ensures they won't be paying full property tax (at least if they've been living there for a while). Even for those planning on living there until they die, their children would still like to inherit a valuable place.
At any rate, I didn't intend to limit the reasons to just price. The solution is to build more housing, but building housing is unpopular, and it isn't hard to see why. So we end up with bad policy like rent control instead.
Or just straight up bigotry. They love to claim apartments increase crime, but then act like row houses are somehow different.