What the court should have asked is, "is a short barreled shotgun and 'arm'?" The answer being an obvious "yes", is therefore protected. Also, if the Miller decision establishes a test of suitability for "militia" use, then why are full auto firearms so heavily "infringed" upon?
the test itself was bunk. the prosecuting attourney had been in WWI, he surely saw millitary using SBSs.
but you ask the same question i do. if -14s, -16, -60, HKs, AKs, FALs, etc are used by millitaries around the world, how do they not have any "reasonable relation to the preservation or efficiency of a well regulated militia"?