At the same time, the military regulation of personal weapons came from past experiences. There are many young, immature, and passionate men in the armed forces, who are very likely to shoot each other in a moment of passion, if they have a gun at hand. The challenge here is to reconcile the needs of force protection against good order and discipline.
It is eminently sensible, then, to allow a limited conceal-carry scheme in our military. Specifically, commanders (O-5 and above) can give their officers and non-commissioned officers license to carry their own weapons in garrison, and perhaps on liberty. Officers and NCOs are [hopefully] more mature than the rank and file. Traditionally, officers have sidearms to enforce discipline, so this policy is a natural continuation. Moreover, officers are to look out for the welfare of their subordinates, making concealed carry a logical extension of that duty. Being at the commander's discretion, this licensing scheme allows commanders to apply their judgement. If a licensed individual is at psychological risk, his commander has the right to revoke the license and place him under observation.
In the field and on deployment, soldiers are issued weapons, so they do not need to carry personal weapons. Personal weapons at war may also complicate the Laws of Warfare.
Of course, today's military, as John T Reed reminds us, is a micro-managing institution that fears the concept of accountability. Even if the generals were willing to delegate such a responsibility, their JAG lawyers will probably talk them out of it. I cannot see us implementing this policy any time soon.