That implies that everyone wants to work, AND that the people who are homeless at the margin want to live in a house. Case in point: I live in a "nice" area up

That implies that everyone wants to work, AND that the people who are homeless at the margin want to live in a house. Case in point: I live in a "nice" area up on a hill in my city and there are multiple homeless who sleep/have camps in the hillside directly adjacent. One of them drives a bmw and has been there at least 6 months. A couple sits in their car all day in the same spot doing who knows what. There are many people who simply do not want to take part in society, while still living within it.