And cost of living will rise with population density
I don't see how you justify this, and therefore the rest of the argument. What mechanism do you see that implies that increasing population density leads to higher costs of living?
I think you are falling into a third cause fallacy mistake. While there is certainly correlation between higher pollution density and higher living costs, it's not one that causes the other, but a third factor that causes both: wanting to move there.
The reason rents are higher is because people are willing to bid more to live in SF; preventing population density will do nothing to curb that desire. But it can reduce costs of living, by allowing rents to drop and therefore reduce the need to bid higher and higher.
Wanting to move there is also a believable cause of high cost of living. But since housing prices are out pacing wages worldwide, I think not. Indeed the NY Times reports 90 cities as "unaffordable" in the US alone.[1]
If there is a theoretical supply and demand argument that building always drives down costs then there is a theoretical argument that excess supply of labor drives down the value of labor.
If there is an observational argument that large population densities do not lower wages then there is the observation that high density cities do not have low cost of living.
My claim is that the price of housing will rise to at least 30% of wages no mater how many or few units you have. If you really wanted to lower rent rather than shuffling around who is living where, you'd need enormously radical change to land ownership laws and incentives. The things that made the twentieth century unique in history for the relative wealth of ordinary people. Things now being reversed.
Another apparently impossible option would be to make other cites into bastions of free thinking diversity, tolerance and creativity so there would be innovation and demand to live there instead of fleeing them for the few cities that have those things and the wealth that comes with them.
But the path we're apparently going to follow, deregulation, which will do exactly nothing, could nicely degrade the character of one city after another which would reduce demand and that might slow price rise. It'd take surprisingly little to turn SF into another Huston. But don't expect the people with a choice to stick around a characterless city among a sea of less imaginative people looking just to get rich quick.
I don't see how you justify this, and therefore the rest of the argument. What mechanism do you see that implies that increasing population density leads to higher costs of living?
I think you are falling into a third cause fallacy mistake. While there is certainly correlation between higher pollution density and higher living costs, it's not one that causes the other, but a third factor that causes both: wanting to move there.
The reason rents are higher is because people are willing to bid more to live in SF; preventing population density will do nothing to curb that desire. But it can reduce costs of living, by allowing rents to drop and therefore reduce the need to bid higher and higher.