I arrived pretty close to the deadline in TPA recently. This was a semi-complicated international itinerary, although the first flight was just to MIA. The check-in agent needed about 15 minutes to figure out whether I needed a visa (aggravating). She sorted it out after the bag check deadline. She wound up taking my bag, but was literally running around the terminal to find her supervisor to override the computer.
TPA is a super easy airport and security was very quick. About 5 minutes after checking the bag, I was at the gate ... and I walked up in time to watch my bag heading up the conveyor to the aircraft.
I get that this is AA's policy. I get that it isn't always quiet enough for a bag (or person) to get through security in less than 5 minutes. But AA knows exactly how long it takes to get a bag from check in to a plane - and it isn't 40 minutes at every airport.
Shame on AA for blindly enforcing a rule that unnecessarily inconveniences a passenger. Doubly so if AA then blames the passenger.
I'm paying AA to provide a service - not for the opportunity to be in their presence.