"Many of these people are mentally ill. And for many of these people giving them a home and money will not solve their problems."

This thinking is based on the fallacy that mental illness is a purely biological condition, which anthropology, epidemiology, and clinical data all soundly disprove. Even for mental illnesses that are mostly biological, like schizophrenia, the quality of outcomes varies enormously depending on the person's social environment as well as the course of treatment.