The Supreme Court did not uphold the conviction of Miller or his co-defendant Layton, because they were never convicted. All it did was rule that the government could put forth a case against them, and that if they wanted to claim Second-Amendment protection they would have to (in the upcoming case) present evidence that a shotgun was militarily useful.
Had the government sought a conviction following U.S. v. Miller, the surviving defendant (Layton) would have had the right to introduce evidence in court that a shotgun was militarily useful. The government basically dropped, the case, however, so Layton had neither the need nor opportunity to present such evidence.
Please tell me how the NFA 1934, the law in question in Miller, can specify a crime, the elements of which include usefulness to a militia, and yet not mention the same.
I would expect the lower courts to rule the law unConstitutional on the basis of infringement of the Second Amendment due to non-mention of the militia connection which the Supreme Court has ruled necessary.
Otherwise, the burden of proof could be moved entirely to the defendant. A person could be charged under this law and convicted for possessing an unlicensed rutabaga after failing to prove that such vegetable was not a short-barreled shotgun.