Actually read Miller. It says that the arms protected by 2nd Amendment are those in common use by the Armed Forces. It is actually the lower courts that stated it allowed the restriction of all weapons. In other words in accordance with Miller as ruled the restrictions on military weapons is not allowed.
In making his argument concerning Miller Scalia says, "it was that the type of weapon at issue was not eligible for Second Amendment protection..." Arguing (correctly, IMO) that The Court was not completely reversing an earlier decision, I still think Scalia goes too far. There is no doubt that Stevens also goes too far, pretending, as gun grabbers always have, that Miller allows whatever infringement on the RKBA a court wants simply by a Sophist's definition of what constitutes a suitable weapon. But regardless of whom you believe was correct, Miller opened the door for an interpretation that a weapon suitable for militia use was the only type eligible for Second Amendment protection. Even Scalia acknowledges that, so you'd be well advised not to pretend otherwise.
The problem is that it is the 1939 decision actually promotes the sort of idiotic bench legislating that George Will decries in this column. One only need establish that a weapon would not be suitable for use in some local (State) definition of "militia" to exclude it from protection. His critique of Heller by proxy is ironically wrong, because Heller effectively tells gun grabbers that they may no longer point to the 1939 decision as a way of making specific weapons ineligible: before Heller, handguns arguably were not "militia" weapons -- whatever that means.
In any event, Miller wasn't even correct as to facts. The sawed-off shotgun was a weapon in common military use. My father was a BAR man during the Second World War. The sidearm he -- and fixed machine gunners also -- were issued, was a sawed-off shotgun. A facsimile of that weapon hangs over our mantle; just below our copies of the Declaration of Independence and the Constitution of the United States.
I read Miller in the epitome or digest, and scanned through the opinion, reading parts of it, and I agree with the point you made. The court made their remand of Mr. Miller (a common criminal caught with an NFA Class II sawed-off shotgun) hinge on the question of whether weapons like Miller's were "militia" weapons. The Court said no -- and the Court fibbed. Shotguns were widely used in the trenches in the Great War, so it erred on a point of fact.
The Court also erred in trying to divide personal sidearms by classifying them, and pretending to rule out the class to which Miller's weapon belonged, for the purpose of a) screwing Miller and b) upholding the NFA and providing the case-law test that Franklin Roosevelt wanted, and which he sent his Solicitor General to get from the unresisting and unrepresented, destitute felon Miller, whose lawyer had quit because Miller couldn't pay him. (Miller's partner was even more disadvantaged: he was dead.)
The language is simple enough: The right of the people to keep and bear arms shall not be infringed, and that includes sawed-off shotguns. The Court lied when they introduced a fictive, fabricated distinction.
There were other points and their sequelae, but that one is the one you were commenting on.