I think the real problem is it's just such a one-sided market in so many places due to market capture by property owners, plus just outright over-representation in lawmaking. If there were a lot more landlords desperate for any renters they can get to avoid going bankrupt on their units, there would be more options for everyone.

As for public housing, there used to be housing projects in the city I live in. The murder rates within those blocks were probably higher than in any country in the world.