Oh there they go again. Building more houses rarely lowers housing prices. Builders will build just fast enough to make a lot of money, and real estate speculators will buy most of that up anyway.
Building more public housing can solve the problem. Banning real estate investment (as in corporate investment) or outright banning owning more than 1-2 homes, that would do the trick.
We know the solutions. All of this has happened before in various places.