This works on a micro scale or closed system but that is not what happens when providing more resources causes people to migrate to your area to take advantage of the resources without ever needing to be contributing to them. A population will simply be over run by those desiring the free housing and this is obvious is any program created like this to tackle the issue. They always run out of room for these high demand resources and eventually cities may have taken care of the homeless problem for the people it meant to, but thousands of new people show up. If it were that easy as just providing housing and the problem was fixed then poverty across the whole world would be eliminated. Not saying that’s not possible, but you would literally have to do that across the entire world or in an entire closed system to make it work.