There are so many different reasons behind homelessness its hard to generalize. It is depressing to read hate filled responses though.
I think it was a YouTube I watched, maybe some thread here had linked to it, but it said something like imagine you are given the power to mold the world to run the way you think it should, but with the caveat that once you had determined it, you would randomly pull your place in the world you created. You wouldn't get a choice just a random selection of what your body and mind would be like, what part of the world you would be born into, the family and financial circumstances you would be born into, etc.
I had a cousin that was homeless, trust me no one would want to employ her or work with her. She was low IQ, stole stuff, poor hygiene habits, etc. I think she probably had fetal alcohol syndrome. My great-aunt and -uncle adopted her from an orphanage in Missouri (she was older than me, so this was back in the old days). Nothing short of a new brain would have made her any better than she was, no amount of motivation to work would have made her desirable to an employer. Was it her fault she was born defective? What is the right thing to do with people like that?
There are so many people with mental health issues, and sometimes brain injuries, or messed up by being raised by crazy people, etc.
It's really a privilege to have a good brain and be capable of appropriate behavior and normal functioning. And it is not something that we should feel smug and superior about, because for the most part we just got lucky.
But, no, I don't think churches should try to be homeless shelters at night, but I think the members of the churches (and everyone else too) should support and encourage adequate shelters and resources.