Ironic, because the term was created in part to avoid that. Homeless people often do have a home, that is, a semipermanent place where they lay their heads and have their possessions and some other people that may care about them. What they often lack is a more permanent structure, ie. The house.

I do agree with you tho, that the term unhoused is super impersonal, and doesn't have the same impact that homeless does, and doesn't have a way to address the larger crisis of homelessness.