The system works in a number of countries. As far as I know, it works. Eventually the only people on the street are people who are unable to cope/deal with the system and who fall through the cracks, such as mentally ill.
Of course one of the costs of any state welfare system is the tragedy of the commons. For example people keeping houses they no longer need and people not maintaing the houses they are in. I would be surprised if the former social problems of slums are improved by bricks and mortar.
I was in South Africa for a vacation recently. They are giving inhabitants of shanty towns small houses. Once they have moved them out they bulldoze the now-vacated land to build more houses.
Someone I met asked me if I could give an old woman a ride to her government provided house at the edge of a shanty town she used to live in. She told me that the solar heating water system installed by the government on all these houses does not work. I could see her house, which could not have been more than 5 years old, was already decaying. I suspect corrupt builders/politicians cheaping out. It was also clear that some of the ever newer houses were quickly deteriorating and were blending into the slum across the small dirt road that separated them, mostly from lack of rudimentary maintenance.
I could not help but wonder what those housing developments will look like in 10 years or 15 years and if the government will have to start rebuilding them at a huge expense.