Because it shifts the burden (or at least appearance) of responsibility from those experiencing homelessness to the government orgs tasked with housing them.
Uh... how does "unhoused" do that? Or, I don't see how unhoused is synonymous with "the government has not provided these people with a house". The opposite of unhoused would be housed. Is everyone that is housed in that position because the government provided a house for them?
Wrongly so I’d argue. It’s your own responsibility to secure a place for yourself (to live, and in society generally). Failure to do this is personal, not collective.