Many people _refuse_ housing for these reasons: (I've been directly told these, or have seen them reported)

* Housing is dangerous/scary (robbery, rape, physical violence, etc...)

* Housing is a conspiracy (to control people or other irrational ideas)

* The rules of housing are too restricting. (can't have a pet, visitors, noise rules, cleanliness rules, curfew rules, behavior rules, etc...)

There are others as well, but can't recall immediately.

A church can't fix these problems, no matter how rich.