The issue here is going to come down to the deterrence perception of having her be armed in those circumstances, versus the legal liability to the bank of having her use that firearm and the criminal liability to HER if she does so.
The Bank Manager wants her to be armed in those few, very rare circumstances for (psychological) “protection”. A deterrence factor in that she’s escorting people with large amounts of money and is armed, therefore deterring any potential criminal from approaching them. Again I will say that unless the firearm is clearly displayed, it amounts to nothing more than a psychological protection. She knows shes armed, the customer may know she’s armed - they feel better. The average joe walking past sees nothing.
Liability wise, the bank is on the hook for HUGE legal settlements in the event that she ever uses that weapon. Unless she has, at the very least, some basic firearms training and is comfortable shooting that weapon, the end result is an accident waiting to happen - and the end of both her career and the bank managers.
Criminal wise, she would have no legal basis to actually USE that firearm in defense of herself or the customer except to defend their lives. If some random idiot ran up, punched the customer in the face and attempted to wrestle away the money, shooting is not a legally defensible option in the great majority of cases. Showing the firearm may be a credible means of stopping the action, but that’s pretty much as far as it goes unless someone’s life is on the line.
The bottom line is exactly as we were told in Armored. It’s not your money. It’s not worth being shot over, or shooting someone else. Let them take it. The bank is insured against this sort of thing.
Hell, if my boss the Bank Manager was presenting these kinds of scenarios, I’d be going to Corporate Security with my concerns. If someone attempts to rob one of my tellers with a firearm, there’s no way in hell I’m pulling out my gun and opening fire. That would be an indefensible criminal and civil liability nightmare fore myself and the bank.
Finally, I have one other issue: Discretion. When carrying large amounts of money, the greatest defense you can ever have is silence and secrecy. If no one knows you have $10,000 shoved in your pocket, no one is going to bother you. But if your idiot bank makes a great big dramatic production of having armed guards escort you to your vehicle, why they just showed the world that you have something incredibly valuable on you and drew a great big target on your head. The thinking criminal is going to follow you to see where you go and if they can catch you unaware at some coffee shop or in your home. (This is an incredibly stupid proposition for the bank and your wife should be working at this angle. Discretion is the better part of Security work.)
Given how many times people followed our armored truck around, which is a lot larger, well armed and prepared target; how easy pickings is that 60 year old woman with the jewelry and the 10 grand in her pocket?