I think the idea is to put the responsibility for housing onto society/authority as opposed to the victim.
Perhaps to some people, but to me it does sound like a homeless person just happens to be without.
Whereas an unhoused person has been let down by whoever is responsible for ensuring people are housed.
I dont see how. If anything, its just a matter of time until you see houseless as being their fault. Because the baggage is something you (and society in general) is adding. Its not implicit in the word itself.