> If developers build more luxury housing, that'll reduce the price of existing housing, such that it becomes affordable.
If the last few decades have taught us anything, it'd that location (and every social category that location encodes) matters to people more than luxury, or rather a desirable location is the biggest luxury.
This is why a 3 BD fixer-upper in Palo Alto will cost more than a luxury 5 bedroom house in East San Jose.
To have any effect on housing prices I desirable places, you'd have to build gobs more housing in the highly desirable places, but those are usually the places most opposed to new housing development. And if you build a little bit more, because location dominates all, the existing housing would be as expensive as the new luxury housing in that location, because there is always a higher demand/supply ratio to live in Palo Alto than for East San Jose.
By the same token, building luxury housing in less desirable places won't change things unless you somehow make those places more desirable, but that takes a lot more than new luxury apartments. You usually have to change the kind of people that inhabit that location.
We absolutely need to build more housing of all categories everywhere, but it won't have much effect on housing costs until we address transportation, public education, and crime, the massive factors that affect housing costs.