This problem has been solved in many countries the world over. I refer you to them. We don't have to reinvent the wheel.
Some hybrid that could work in this country is probably required here.
I have visited some of these countries where they have "solved" this problem. The people live in shanty towns of free housing where there is no land-ownership and no social program support from the government. These countries are third world wrecks and the people living in the "free" housing are desperately poor. Should the U.S. sink to this level? Should the next shanty town be placed next to your current home?