Sir Robert Peel, considered to be the Father of modern policing, noted that there is a historic tradition "that the police are the public and that the public are the police; the police being only members of the public who are paid to give full-time attention to duties which are incumbent on every citizen, in the interests of community welfare and existence."
Slinking away and "being a good witness" when you have the ability, the means, and the training to put an immediate end to an imminent deadly threat against the life of another means that you are shirking your solemn duty as a citizen of our society.
Sir Robert Peel died 150 years ago. Firearms were not prevalent in crimes in England then. What firearms there were fired one or two shots. Most incidents like the above scenario would have involved a knife. Most men if they had money would also have carried a cane as part of the dress code. Sword canes were very popular back then. People without much money would frequently carry knives and impact weapons. The chances of someone other than those involved in the fight being injured were much smaller than they are today. Every bank, store or other business establishment where a stickup would be likely that I've ever been to usually has several people inside waiting to make a deposit, cash a check, make a withdrawal, or pay for their purchases. There are usually several employees on top of that. Any handgun that is powerful enough to have a good chance at incapacitating someone rapidly, is also powerful enough to shoot through someone. People when they panic are likely to move. Then you have the fact that you or the robber are likely to miss with some shots. If one of you is hit, there is a possibility you will fire a shot or shots involuntarily as a result. There is also the posibility that when you surprise the robber he will fire. Keep in mind most people in a bank, store, business establishment are going to be in a relatively small are around this. I'm a LEO and in that scenario I would call for backup and just wait and observe unless he was acting as though he was going to shoot someone or there were very few people present and the robber was acting rationally and calmly. I think it's a lot better to lose some money than get someone killed or injured when the possibility of that happening is less if you do option b(call, wait, and observe) than if you do option a(fight it out).