So the solution to government interference in the market (by preventing adequate building from occurring) is yet more interference, and that interference will by fiat somehow lower prices, but without dramatically increasing supply.
The government isn't preventing anything, it's a free market. The only thing that needs to change is to prevent companies from buying houses meant to be sold for ownership who then rent them out instead. That is working against the people. The law would work for the people.
What could possibly go wrong??