So, what you are saying is that the "common use" test in Heller would have to be specifically applied to the AR-15 by SCOTUS?
Not exactly, but sort of. The issues arises from a combination of what I call "court speak" and the various agenda driven people in different departments and levels of government (Fed, State, city, etc) believing that they can do any/everything not specifically and clearly prohibited by SCOTUS.
In District of Columbia v. Heller (2008), the U.S. Supreme Court held that the Second Amendment protects “arms ‘in common use at the time’ for lawful purposes like self-defense” and arms that are “typically possessed by law-abiding citizens for lawful purposes.”
Now things get a bit tricksy, because there is the actual ruling on the case (Heller vs. DC) which said DC could not ban handguns. The reasoning behind that ruling is explained by the "in common use" language. But its not the actual ruling, directly, its a part of it, and one that the anti gun people easily "break off" and essentially, ignore.
Additionally, the court speak of the explanation gives them what they see as a loophole. Translating the court speak (a bit) the part about items in common use, and the part about other gun control laws being "presumed legal (Constitutional) is related to the (intentionally) overlooked part of the explanation where they essentially said, "Since we're not looking at that, today, we will presume them to be legal, and the implied "until we do look at them, directly".
THIS is how the court works. They look at the issues, in a specific case, and make a specific ruling. THE REST OF THE COUNTRY grabs that specific ruling, or the part of it they want, and runs with it as a general rule.
One of the huge historical examples of that was the Miller decision on the 1934 NFA. That court ruled that "since we have been shown no evidence" (and, they weren't) that the sawed off shotgun in the case was not a milita weapon and therefore not protected under the 2nd Amendment.
That's literally, all they ruled, but the rest of the country took that to mean the entire NFA was Constitutional and we've operated on that ever since.
Another point, widely misunderstood by the general public, is that SCOTUS is not required, and will not "correct misinterpretations" of their rulings. Doing that isn't their job. That is the job of the lower courts. SCOTUS won't get involved, unless a specific case comes before them where an interpretation of a previous SCOTUS ruling is involved. And that is something that happens when there is a "circuit split" as well.
One of the things Heller said (boiled down a bit) is that DC could not ban an entire class of weapons. But "thou cannot ban" is NOT "thou cannot restrict" so we are in a situation where what we are sure the court meant and what others think the court meant are different, and the court will not say who is right, (again, not their job) until a they rule on a case that directly covers this issue.
I believe that until we get a SCOTUS ruling that specifically says "you may not restrict AR-15s (or "assault weapons" or some similar term) there will be people trying to restrict them. And, I suspect, that even if we got a ruling that said those exact words, we'd still have people trying to work around that.
All for our own good, of course...