No it's not impossible. The state can go in and build houses and rent them out and because it's the state there doesn't have to be a profit motive. I used to live in social housing for 8 years and thought it was great. However if there is no social housing construction and private investment is needed to get more housing built then there has to be a profit motive else no one will be motivated to build. However I'm against exorbitant rents. There has to be a balance. No profit at all (+no current social housing program) simply leads to no housing. At least not rental housing. People are of course free to build their own homes but that's not the solution either as not everyone has the money to do so.