Precisely! The real discussion is how much would it decrease supply and what impact on the homeless rate would occur per unit change in labor input cost. Discussion of good/bad/better/worse is fruitless. We need data. But you take the first step by acknowledging these are related costs and social outcomes that exist in a delicate equilibria. Many would just say to heck with unintended consequences it's a matter of principal or ideological mandate. Gotta break a few eggs types.
Your discourse is sensationalist and unnecessarily agitated. Paying workers a fair wage wouldn't triple housing costs, that figure is completely made up.
> We'll all be homeless
It also wouldn't lead to complete homelessness.