I think what would happen is the hordes of people who are not remotely qualified, e.g. folks looking to move on from receptionist positions, tech support people

I think what would happen is the hordes of people who are not remotely qualified, e.g. folks looking to move on from receptionist positions, tech support people from less prosperous nations looking for visa sponsors, etc, would continue to shotgun their applications. And qualified people wouldn't bother.