Did you post the citation stating the ban on sawed off shotguns was because of a lack of control or did I miss it?
No, the direction given in Miller case was that restrictions can be placed on arms that are "dangerous and unusual."
It's a somewhat vague terms. All weapons are dangerous. Period. I hope we can agree on that.
Anything not in the hands of at least 50% of the population could be considered "unusual" and thus any new model of weapon to market would technically be unusual.
Thus the term is a bit misleading without the direction given behind it. Dangerous is based on control of the weapon. Which goes back to the definition as stated in both Miller and Heller of what the definition of
arms is. Arms at it base they both state is any weapon capable of being used in the arms of an individual. But that is still a slightly vague definition. Thus they go into various other more nailed down definitions as well as various writing by the founding fathers of the meaning they intended when they wrote down that word arms.
The meaning was for a controllable weapon that can be wielded by a single person. THAT was stated to several degrees in both the Heller and Miller cases. Heller went more to expound upon how the 2nd amendment is for 100% sure an individual right with its dictum and exploratory explanations.
The National Firearms Act put restrictions on several categories of arms by stating they were dangerous in use. Those were machine guns, short barrel rifles, and shot barrel shotguns (long gun variety). The argument as to their danger is that those were weapons that could make the operator lose control while firing. It's a bunch of bull crap, but that was the argument made. Heller just references this without going into detail. You have to read the original arguments for the NFA to find this out.