It would not. The Miller decision has been intentionally mistated by lower courts for almost three quarters of a century.
The prosecution in Miller asked, in its Summary of Argument, that the Court find that only militia members were protected by the Second Amendment.
The Miller Court did not agree with this argument, which would have rendered the type of arms irrelevant in the Miller case, since Miller and Layton were neither one associated with any militia. There was no suggestion that Miller or Layton could claim militia membership as protection against prosecution. The only evidence that the Supreme Court noted was lacking was with regard to the particular short-barreled shotgun possessed.
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I thought they ignored the argument. Can you please point out where the Miller court disagreed?