Wrong!
Short barreled shotguns, often double barreled ones, were common among horse calvary units, and would be suitable for today's mounted troops as well, in some situations. Just because the US Army has decided to go with short barreled M-4 Carbine versions of the M-16 rifle, doesn't mean other weapons would not be suitable as well. The P-90, either select fire or semi-auto versions, to name just one example.
Remember that the Supreme Court never ruled that a short barreled shotgun was not suitable for militia purposes, but rather that the lower court should not have ruled that is was, without taking some evidence to that effect. IOW, they should not have taken "judicial notice" of the fact that it was, or was not, "Part of the ordinary military equipment"
Of course if Miller had been armed with a BAR or Thompson, things might have been different. Even the Supreme Court would likely have decided that those were well enough known as military weapons to allow "judicial notice" to be taken.
Wrong!
The lower court never ruled that Miller's weapon was or was not suitable for militia use. They said the NFA violated the second amendment. They were no more specific than that.
"Short barreled shotguns, often double barreled ones, were common among horse calvary units"
The shotguns used in WWI were 20". Now if you want to make the argument that the Pilgrims used a 16" blunderbuss, fine.