Here we have the issue of when does a flight actually leave? If the airline says it has left because it has left the gate, when you are sitting on the tarmac for an hour and a half, waiting for wheels up, then any reasonable person would say that the flight has in fact not yet left.
The twofold problem is this:
(a) How to make phone agents understand what's going on. It's quite ridiculous that the phone agents can't check up on Flightaware, or similar, to see the status of the plane, if the airline's own system cannot see that the plane is still parked at a holding apron. That's what I'd ask them to do.
(b) Gate agents book a flight out when it leaves the gate. They don't hang around to see whether it actually takes off. IMO this needs to change. Gate agents should be "responsible" for the flight until it physically departs, even if they are handling subsequent departures. Otherwise you get the scenario (as happened to a friend of mine recently) when the last flight of the day is delayed taking off, and eventually returns to the gate and is canceled because of a mechanical. Long before then, the gate agents have packed up and gone home, and there is no one left at the airport to service the passengers' overnight needs and get their luggage back, let alone rebook them the following day.