If you have been watching California's experiments with homelessness, especially San Fran. you may have learned that homeless people prefer being homeless even when given free accomodations and when i say accomodations I mean nice hotel rooms of their own.
This is because homelessness is a side-effect of mental illness and drug addiction. The later is not all drug addiction, ( I used to live next to an "invisible" heroin addict which we only learned about when he OD'd) it's a certain type of disorganized-thinking and lifestyle which some addicts manifest.
The cost of housing doesn't cause homelessness; it causes roommates and the conflicts and violence and chaos that imposes on people's lives which is significant if under-studied.