Have had this happen a couple of times, most have been rebook on the next flight or re-routed to another airline if it was more than a short overnight or no hotels available (tech mostly on this). However at least twice they've held the plane for to around T+10ish, both on MIA-STX when the corporate travel people raised a ruckus for me to catch a ship. My guess that there was something in the contract between the company and AA about delays.

Not quite as spectacular when the US Navy had UA pull a 747 back to the gate because they didn't want to move me after they had an indicator light burn out at SMF and they didn't rebook me to one of the two flights in between from SMF to SFO. Sometimes the mention to OPS about a $100k bill to heading their way gets things moving.

Of course if the OP really want to cause a stir then email CS about the open gate with no agent and cc: the TSA...