Why is it obvious getting rid of Airbnb won't reduce housing costs? All else being equal, it could increase supply if the hosts are holding on to them only for

Why is it obvious getting rid of Airbnb won't reduce housing costs? All else being equal, it could increase supply if the hosts are holding on to them only for renting. Increase supply = reduce cost, no? Edit, and by cheaper, I mean less than they would be otherwise. Maybe that's the confusion I'm having.