To quote the last sentence of the comment you're replying to:

> Prices could stay high, however, if more people move to the area, increasing demand to match supply.

I think that's key. Places that are seen as the most desirable to live in tend to attract people. If housing got (temporarily) cheaper, more people would move in and it would return to a similar equilibrium.

I think this problem is best fixed by creating more desirable places to live, not by trying to find a way to pack more people in (though efforts to reduce housing prices are admirable and worth doing).

Something I've wondered a lot about is if it's possible to create desirable cities deliberately, rather than let them spring up naturally. (Obviously a lot of developers have tried to do that as a way of making money, but I suspect you could get better results if you set out with the primary aim of creating a pleasant place to live and work and structured it as a non-profit.)

>by creating more desirable places to live, not by trying to find a way to pack more people in

There's effectively infinitely much suburbia in America already. It's the "packed in" experience (walkable streetscapes, transit-connected mid- and high-rise housing, etc) that's scarce, and that we need more of.

If one believes density is a good thing that makes for better living, then adding more units should make it a more desirable place to live, driving more demand, and increasing prices. SOMA might be an interesting example of this, where it used to be cheap and undesirable, but after a critical mass of housing was built, it became much more livable and expensive. Of course, there are hundreds of things having simultaneous impacts, so it is impossible to isolate the effects of one.