You might not like where that logic goes. The Supreme Court took a stance in United States v. Miller (1939) that the NFA’s provisions on short barreled shotguns could be enforced on the basis that it’s not a weapon that would be used by a well-regulated militia.
That brings us to a conclusion that literally nobody likes. The government could ban shorty shotguns and .22 rimfire, because those aren’t militia weapons. It could not ban fully automatic weapons or even rocket launchers.