Country-wide population density is a shit metric for what we are talking about. If the US annexed Antarctica tomorrow population density would plummet but it would be almost entirely meaningless in the foreseeable future in the context of a discussion on zoning laws.
The point is that this turns into a discussion of zoning laws because of an obsession of increasing density in hotspots, despite the fact that you have vast areas of viable land that is cheap, with few zoning restrictions, and far more viable to built extensive infrastructure to/from/in.
High property prices is not all that much of a problem unless your goal is the highest population density possible, or for you personally if you're dead set on living there. Rather, it is a market mechanism that if left to work will push the population further out, and benefit people in a much larger region that way.
Zoning is a problem mostly seen from the outside: Of people not living there who don't like that the locals believe the character of their neighbourhoods is more important than opening up for higher population density.
As much as I can sympathize with the desire to live somewhere that is "taken" at a price suitable to you, that's never something you will be able to do without some restriction or other. And the reality is that for a lot of people, those places would be ruined forever if there was nothing holding back rampant development.
