On-duty military personnel are generally uniformed, and thus already advertising themselves as serving in a military capacity (just like uniformed police officers and security guards). A mom doing back-to-school shopping in a crowded store with three young children in tow is a totally different story. She is by definition distracted, both by the purpose of her outing, and by need to keep an eye on the children. She is thus an easy target for someone looking to grab her easily visible gun, either by stealth (less likely, but not impossible, when you consider how often handbags get lifted of the back of a restaurant chair that the owner is sitting in), or overtly, by somebody bent on murderous mayhem followed by suicide.
I think you’d find plenty of situations where special military forces (and police and security guards) engaging in covert operations (i.e. non-uniformed), are indeed carrying concealed for tactical advantage.
Is that really where you want to take this discussion?