Earlier quoted context omitted.
New construction has already decelerated in Austin due to falling prices, which compresses already-near-zero margin on real estate development. So yes, it really is "just build more housing." The problem is: why would you build more housing as prices fall?
I'm confused by this objection, if you draw a stereotypical supply and demand curve, you can see how prices settle to an equilibrium point. Of course reality has more complications, but I think your objection is 95% answered by a supply and demand curve. You keep building houses when it is profitable. You stop when it is not. This naturally keeps everything in balance.
Markets don't optimize for "everyone gets some", yet that's precisely what you need for housing. You'll always need the government to come in at some point to provide for those left behind by the free market.