An M-16 is barely state-of-the-art as individual battle arms go.
They hyperbole of Nuclear weapons or other WMDs in private hands (the equivalent of a Ship of the Line in colonial times) does not change the fact that currently permissable arms without special permit and fees, are well behind the curve of the average infantry battle rifle today. Some weapons, by their economic demands become primarily the equipment of governments--private individuals can neither afford to feed nor maintain them.
"We are not talking about privately owned warships, or even cannon, but the arm a soldier carries into battle. "
On the contrary. Those were legal too. In fact, that legality is implied by the power Congress possesses to issue letters of marque and reprisal.
You wanted a ship of the line? You built or bought it. You wanted cannon? You bought it.