Covenant me old.
I think you're wrong on this one. If we reach the stage where someone is breaking down the flight deck door, then if we lose the fight for the flight deck it is all over. It doesn't matter if the bad guys end up with a firearm or just a dangerously sharpened toothpick.
As far as winning the fight goes, I'd rather trust my strictly average skills with a handgun than my below average hand to hand capabilities with the crash axe. All your points about the stress of having to make that decision and do the deed for real are well made, but they apply even more so to hand to hand.
In a 'door breakdown' scenario, the door isn't going to evaporate. There is going to be a period of time where it is partially breached, allowing the crew to shoot out at a range of a perhaps 2 feet, but not permitting improvised clubs etc to be used in reverse. Simply bringing the weapon in the field of view of the terrorist would most likely make even the most dedicated suicidal attacker flinch and take cover for a while, even if you couldn't get a shot off, and every second will count because one of the good guys will be getting the aircraft on the ground ASAP.
Fundamentally, every defence can be breached
and this is why a layered, secret and unpredictable strategy is essential.
You'll remember the principles of war. Derivation of tactics depends on knowledge of enemy intentions. If the terrorist doesn't know our intentions, then it is difficult for them to come up with a plan.
CPB