My experience is mostly with United; they've almost always asked volunteers to wait in the boarding area. I'd imagine it slows down the take-off if they have to go on and get passengers (and see if they're still interested); the way things stand they can give the overflow boarding passes immediately and try to get out reasonably on time (not too likely with an overfull flight ).

To my mind the full overheads is simply a risk of volunteering, well compensated for by the frequency that I've been upgraded on my replacement flight.