No, not at all, nor is concealed or open carry right by me, because of exactly that reason. If we want to say that the state doesn't get monopoly on violence, I don't see any logical reason to limit that simply to a handgun. IMO every person, in such a world, should be allowed to arm themselves with nuclear weapons. Absurd but I see no difference between that and guns other than scale of destruction (and the scale is still enormous for a gun).
Sure, if a law-abiding citizen was trained and followed the military nuclear safety procedures, could actually afford said nuclear weapon and implementation of all applicable regulations along with appropriate inspections and all applicable oversight and background checks, I honestly wouldn't care if they had a WMD.
At that point, there is little difference between between a military officer having access or a citizen having access.