“When was the last time you saw a gate agent reopen the door?”
How about last week for me? I got to the gate 15 seconds after the door closed (I saw it closing) and they reopened it. It was the last flight out for the night and they would have had to give me a hotel voucher since it was there fault for delaying the inbound flight. I’ve also seen them reopen the doors a number of times on international flights. I’ve never seen them open a door though once the aircraft door was closed, except once on an international flight.
The aircraft door was what I meant. Until the aircraft door is closed, it's not usually a significant burden for them to allow a passenger on the plane.
I believe that the warnings I remember of boarding passes mentioned that the no one would be allowed to board after the aircraft door had been closed.