That's not what Miller said. Here's what the court found:
"In the absence of any evidence tending to show that possession or use of a 'shotgun having a barrel of less than eighteen inches in length' at this time has some reasonable relationship to the preservation or efficiency of a well regulated militia, we cannot say that the Second Amendment guarantees the right to keep and bear such an instrument. Certainly it is not within judicial notice that this weapon is any part of the ordinary military equipment or that its use could contribute to the common defense. "
They didn't decide the issue. Since no one showed up to argue Miller's side of the case, they just remanded the decision and told the lower courts to work it out.
Scalia discusses this exact point in his decision, and opened the door wide to future litigants seeking clarification. This may seem petty on my part, but the distinction is important as the issue is still in play, and will doubtless come up in the near future.
Molon Labe!
From your post: Certainly it is not within judicial notice that this weapon is any part of the ordinary military equipment or that its use could contribute to the common defense. "
This is why I said the court made a mistake - they didn't do their homework. Maybe it was - as you said - a result of Mr. Miller (who I believe was deceased by the time the Supremes heard oral arguments) had no one there to actually represent his side.
In any case, they were wrong about that. Sawed off shotguns had been used to great effect ALREADY in WW I. Not to mention bootleggers found them very useful for illicit perposes, when they couldn't get their hands a the sub-machine guns of those days.
So I again state my point that the USSC was unaware of the LEGITIMATE use (or uses) this type of weapon could have. During war, or as home protection, and on and on. They didn't do their homework, whether Miller had an attorney present or not, and they screwed up.
And whatever lower court looked at this case on the way back down ALSO screwed up. And for several decades now, somehow this case has been used by the anti-gun crowd to say some really stupid things.