Your church down the street is not equipped to handle the mental health issues that often accompany homelessness.
While I do believe charity is better placed in the hands of churches and individuals, and not left to the works of the state, mental illness treatment should not be a community effort of the church, in most cases.
When some of us older posters here, were younger, mental health issues were swept away, to facilities made to care for them. Today, mental health issues are not swept away, they are swept aside, allowed to linger, fester, and work themselves out. Treatment is often outpatient, or ignored. Treatment today is more pharmaceutical, and not so much nurturing development. Kids in school, that are "Hand Fulls" are not given extra laps around the gym, they are handed pills by the school nurse. This turns into lifetime dependence on medication and reliance on treatment.