FWIW I know that in some rather remote areas businesses often don't have real addresses valid for mailing, this was common on the Reservation I used to live on (Alcon has reported it's common on other Reservations, even for private addresses.) Some also have addresses but can't collect mail there (The main thing that comes to mind is a strip club I know of, lol, but it still counts.)
And I don't see how this'll work anyway, the proposed change still leaves a pretty big loophole. There's tons of cheap office space, they can just rent out a room and hire a receptionist to handle basic duties and now they have a headquarters.
This what I was driving at above. It is hard to create hard core regulations that will successfully deal with the problem. It is even harder to craft those so as to not crimp legitimate business activity.