Yes, but you are singling out a weapon. The way laws work is you need to define what people can't do. So you still need to define it, for either a ban or strict regulation.
NFA 34 defines what you can't have, and what you need to do if you want to have it. It defines automatic weapons, short-barreled weapons, and sound suppressors, and no dice unless you pay the tax and wait 8 months (I won't go into destructive devices as that's no longer "small arms"). This is easy, weapons that fire more than 1 round per trigger pull, barrels with less than a set length, and devices that reduce sound measurably.
So you want to define the AR-15.
Okay, let's start with manufacturer...okay let's not, because everyone makes one these days, it's as close to an open source weapon as there is.
Okay, what about model...oh wait everyone names it something different.
Caliber? Not really, .223 is a common varmint gun caliber used in bolt action rifles. Also AR-15s can and frequently do use other calibers for various applications from smaller than .223 to as wide as .50.
The only way I could see getting away with it is dimensionally defining an AR 15 by the required tolerances for operation of parts designed for it, but you can see the loophole for that coming a mile away (a new set of unregulated dimensions will be settled on and manufacturing will resume).
California tried this, they have a big old list of shit you can't own. The courts told them it had to be by "make and model", you can't list a "series" of weapon as that's too nebulous, which made the list basically useless. Then they tried banning "features" like the type of grip or muzzle device or type of stock for semi-autos, which was worked around in a matter of years (look up "bullet button AR 15" if interested").
Okay so maybe getting more specific isn't helpful, what about getting less specific?
So what about semi-auto rifles generally?
Well you'll run into a wall with 3 court decisions in all likelihood, and one of them advantages the AR-15 specifically.
First Miller v United States (not the porn one, the less than 18 in barrel shotgun one) brought about "common use" as a measuring stick for whether a weapon merits judicial protections, and the AR-15 has undoubtedly come to be in "common use", I think the fact that it is in "common use" is one of the few things we can agree on.
Next you need to deal with Heller and McDonald, which speak to a broader change in 2nd amendment jurisprudence that recognizes the 2nd amendment is incorporated into the US constitution under due process (meaning the feds can bat down a state's law) as well as movement away from the antiquated "muskets" paradigm which never made sense (remember, just because new tech comes along that doesn't change the meaning of the law, logical consistency dictates that if the internet gets 1A protections, new small arms in common use get 2A protections).
Also be wary of trying to find a way to define the AR-15 as uniquely dangerous, as there's a trap in there. Remember that the M-16 was designed to use rounds that were "good enough" to kill people, not because the rounds or the gun's design were uniquely deadly TO people (they aren't, the .223 is considered a "varmint" round, i.e. fast, flat, and small, designed to shoot prairie dogs).
The M-16 was a logistical calculation based on the changing face of combat at the time:
-Rounds are heavy, if you can carry 60 rounds OR 20 rounds and they both put holes in people with guns trying to kill you, I'll take 60 (which would be the M-16). It doesn't hurt that smaller rounds makes magazine capacity higher at similar magazine size a possibility. This is to say nothing of the supply chain benefits of reduced weight by volume.
-Power leads to recoil, and recoil makes it hard to hit things, an added potential advantage of lower powered rounds.
-Most combat takes place within 600 meters, and engagements at longer distances can be dealt with using other weapons.
-Humans are extremely soft and poorly protected.
Basically, as the AR-15 is just a semi-auto variation of the M-16 design, it's a semi-auto rifle that usually shoots a round with ballistics designed to kill prairie dogs, and it so happens that humans are only somewhat more durable than prairie dogs. You won't find a "too powerful" because it's design is the antithesis of "too powerful". It wouldn't even be a reach to say it was designed in response to "weapons of war" being "too powerful".
Just some food for thought.