The American Bill of Rights; first 10 amendments to the U. S. Constitution, are restrictions on what the government can do to the people, not stuff the government has to do for, or give to, the people.
"In all criminal prosecutions, the accused shall enjoy the right to a speedy and public trial by an impartial jury of the state and district wherein the crime shall have been committed, which district shall have been previously ascertained by law, and to be informed of the nature and cause of the accusation; to be confronted with the witnesses against him; to have compulsory process for obtaining witnesses in his favor; and to have the assistance of counsel for his defense."
Written a different way, this would say "the government can't take away your freedoms by arresting you, accusing you of a crime, but then delaying or denying a fair trial to figure out if you're actually guilty."
That's still far different from the government being obligated to provide you housing.
(To be clear - I'm not taking a position on universal housing. It might be a great idea! I just think it's a different class of right, and I think the distinction is worth preserving.)
I see, I always thought that those amendments were about equality between people, but in this context it makes more sense.
Your right to freedom is what's at stake. If the government wants to take it they agree to make their case, not do so capriciously.
The harsh logical truth is you /always/ pay for other people in some way. Choice only affects the cost and outcome.