No, you need a government agency which will build social housing.

Not once has the private sector ever been "encouraged" to build social housing with deregulation. The only reason it keeps getting touted as The Solution in the media is because deregulation would boost their profits.

The bottleneck is land, anyway. If you dont tax that enough or take it with eminent domain then you'll end up like San Francisco with absurdly low density housing and criminally high rents.