My recollection of the Miller decision differs from your description.
As I recall, the government made two arguments in their attempt to overturn the District Court decision in Miller's favor; that is, the District Court had decided that Miller's keeping and bearing of a short-barreled shotgun was protected by the Second Amendment.
First, the government argued that the protection of the Second Amendment applied only to members of an organized Militia. Second, they argued that the protection of the Second Amendment extended only to arms that are useful to a Militia.
The first argument was never addressed directly, but the Supreme Court obviously rejected it. Otherwise, since Miller was not a member of an organized Militia, the Court could simply have said so and the case would be over and Miller would have lost.
Instead, the Court accepted the second argument by the government; that is, that only weapons that are useful to a Militia are protected by the Second Amendment.
The Court was provided with no "judicial notice" regarding the usefulness of short-barreled shotguns, so they vacated the ruling by the District Court that had been favorable to Miller and remanded the case back to that lower court in order to decide about the usefulness of a short-barreled shotgun.
For various reasons, the lower court never took any future action. Despite that, other courts mistakenly and maliciously misstated the Miller Decision and invented the "collective right" nonsense that prevailed until the Heller Decision.
Although I think the Heller Court attempted to make it appear as though they were not overturning the Miller Decision, I think that they were.
The Miller Decision was that ONLY weapons useful to a Militia are protected. The Heller Decision ADDED Second Amendment protection for arms that are useful for self-defense.
Perhaps we can look forward to a Kavanaugh decision that recognizes that AR-15s are THE militia weapon of the twentieth century and are therefor protected. That could be fun.
I know that there was a lot of emphasis on the usefulness of a short-barreled shotgun for militia purposes, but the case ALSO relied upon the ability of the Feds to regulate firearms.
Check out this analysis of the Miller case:
http://migration.nyulaw.me/sites/default/files/ECM_PRO_060964.pdf
On page 26 of that .pdf, near the bottom, and going on to page 27, is the following:
“In any case, McReynolds began Miller by emphasizing the
NFA satisfies the Tenth Amendment only because it is at least
nominally a tax, rather than a regulation. 193 As the government pointed out, “even as to this class of firearms there is not a word in the National Firearms Act which expressly prohibits the obtaining, ownership, possession or transportation thereof by anyone if compliance
is had with the provisions relating to registration, the payment of taxes, and the possession of stamp-affixed orders.” 194 So, whatever it holds, Miller does not hold that Congress can regulate firearms directly. The rejection of Millers Tenth Amendment claim highlights the implausibility of his Second Amendment claim. Miller could not just argue that the Second Amendment guarantees the right to possess and use NFA firearms. He had to claim it prohibits taxation of NFA firearms. Unsurprisingly, McReynolds found this claim unconvincing. Whether or not the Second Amendment guarantees an individual right to keep and bear arms, it hardly prohibits Congress from taxing particular weapons.”
BTW, don’t assume that I agree with the “Miller” case - I find it an awful case which perhaps had some utility (in the pre-”Heller” world) to fight gun control, IF you could craft the right case and make certain that the firearm in question undoubtedly had “utility as a militia weapon.” Of course, now much of “Miller,” if not the entire thing, is pretty much moot. I look forward to a case after Kavanaugh is confirmed, as I believe that many of the issues that both “Miller” and “Heller” avoided will be addressed. As an Originalist/Textualist, Kavanaugh is VERY well aware of the Article 1, Section 8 power that Congress has to grant “Letters of Marque and Reprisal,” which necessarily presume the private ownership of naval cannon and warships (or commercial ships converted to warships) with which to attack enemy shipping. Such a “big view” of the 2nd Amendment will, IMHO, render the entire NFA unconstitutional...if you can own cannon, why on Earth can you be prevented from owning full autos, suppressors, sawed-off shotties, etc.?