At least around here, I'm told by several reliable sources that there is plenty of housing for the homeless, both shelters and Section 8 apartments and other kinds of places. They point to the problem I've been discussing.
Take some woman subject to physical abuse and has to leave her husband and his house (or their house). She's literally out on the street unless she has friends or family to take her in. She needs shelter, beyond maybe her car. Give her two kids. That issue is generally well managed, at least around here, and they can get her up on her feet relatively quickly. But then she is replaced, as I say, with another similar situation. So, the numbers show a lot of them being homeless, but their situation is manageable, UNLESS they are drug addicted or insane, which is generally not the case.
If we walk 3 miles here, which is normal, we'll see 2-3 homeless, nearly always men, nearly always black. They are VERY difficult to help. One agency here has a good track record even with them, but they are unfortunately small and have high requirements most of these men can't accept.