In your posed bank situation, though I think it would be a stupid and irresponsible move by the bank, I still contend that the person responsible for the robbery is the robber, not the bank. Is the bank required to not make it easier for a criminal to do his criminal act? They did not hand the gun to the felon, the felon picked it up of his own free will.
If I own a swimming pool, I am obligated to fence it and lock the gate or being violation of ordinances and face personal liability for injury or death to a second party, even if they were not invited. I must actively protect others, whether they have permission to be there or not.
A bank (or other merchant), on the other hand, assumes no proactive position to protect my safety from criminal injury. They espouse the faulty logic, "just give him what he wants and he won't hurt anybody." Unfortunately, we know how that works out sometimes.
The bank maintains that their losses are covered by insurance. Tell that to your spouse, significant other, or parents when you do not come home.
The banking industry is perhaps the only business type of which I am aware that can make repeated insurance claims for the same kind of incident without having radical increase in premiums or being charged to make improvements to reduce re-occurrence.