I'm not sure what the point of doing this is. It reduces rents for current tenants but doesn't increase housing stock in total which is what is really needed to bring rent and purchase prices down. \
Throwing more units onto the market as it is just invites more speculators, small landlords and AirBnB micro-hoteliers. The incentives for profit and speculation need to get quashed first. Reducing prices for some units will ultimately reduce prices for others in the area, helping make both purchases and rentals more affordable.
This is a much better idea. And I've heard several housing advocates push for a public development agency whose job it would be to basically do all the work necessary to accelerate and/or build in the public interest either by assembling land, upzoning or providing loan guarantees or taking equity stakes in development.
I agree; we need more investment into properly sustainable public housing. But we also need to follow examples like those in Finland who for a long time have pushed that 25% of all new housing must be affordable, or Sweden where half of all rental units are publicly owned—meaning the government leads the market, and isn't just forced to exist solely for those who can't afford what the private market decides rent should be.