Actually, I did the math a while ago for Syndra (you know, super bursty) and just any ADC at mid-game. Let me go find that post really quick.
Okay, let's do a 10 second recording at mid-game.
ADC:
1.6 AS, 250 (half-build AD) AD, 20% crit.
So, in 10 seconds, we get: 6.25 (10/1.6) * 250 = 1,562 damage. Now if we assume 20% of those crit (dealing double damage) , we get 625 (crit AA) + 1250 (normal AA) = 1875 damage.
That's 1,562 damage over 10 seconds with no crits, but 1875 damage over 10 seconds assuming a 20% crit rate.
Syndra:
Now, let's look at Syndra, someone who's very bursty, and is 75% skillshots.
This is assuming about 10% CDR and 250 AP.
Q: ~320 damage.
W: ~200 damage.
E: ~120 damage.
R: ~500-800 damage, depending on how many balls you drop.
So, the basic Q>W>E>R 4-ball ult rotation, which takes about 5 seconds.
~320 + 200 + 120 + ~650 = ~1290. So, in 5 seconds, Syndra wins in damage, since an ADC would only do ~940 at this point max.
Now, how about a 5 ball ult, which requires a bit more effort on Syndra's part?
Q: ~320 damage (x2)
W: ~200 damage
E: ~120 damage
R: ~750-800 damage.
640 + 200 + 120 + 750 = 1,710 damage. This combo takes about 8-9 seconds to land (since you have to wait for your Q CD to come up, and then your ult takes time to deal its damage.
So, Syndra (who has to aim everything she does, and has to manipulate her balls to make her ult do any kind of respectable damage) can do ~1700-1800 damage in 10 seconds, assuming she lands every skillshot and doesn't mess up her ult (which is kind of likely).
Meanwhile, an ADC (who can't miss, doesn't aim, and can just click and AFK) does between ~1600 and ~1900 damage depending on their crit rate.
Let me repeat that: Syndra's potential damage in 10 seconds: ~1700. ADC's potential damage in 10 seconds: ~1600-1900 depending on crit rate. -- and this isn't even including the damage an ADC gets from abilities; this is JUST AA SPAM.
So, yeah, even mathematically, an ADC is VASTLY superior in any fight over 6 seconds (which is, you know, most of them). A late-game ADC with nearly 100% crit, 300-350 AD and nearly 1.8 AS though? Let's do the math there!
In 10 seconds, a late game ADC would do nearly 3700 damage, assuming an 80% crit rate, 1.8 AS and 350 AD (which is VERY likely). And that's not even counting things like Rapid Firecannon, Statik, masteries, or any of that.
Now if we want to look at broken, I could do a figure for Yi, with bork, his double strike, Devourer and all that. Just to show how broken he is.
So there's my little math session I did for another post of mine a while ago. So, yeah, if a fight lasts less than 5 seconds, a mage MADE FOR BURST could potentially beat an ADC -- but Ori has like half the damage Syndra does, so the ADC would just hand her ass to her. And Azir isn't burst anyway, he's a sustained damage / poke mage.
As for counterplay, do enlighten me, how do I counterplay an attack that cannot be dodged or prevented in any way?
And, no, every champion's auto attack does physical damage. Some champs, like Ori, Tahm and so on, have extra magic damage (purple, by the way, not pink) added onto it. The actual auto attack is still physical.
Yeah, so those AA-centric champions would have to build for AA damage. Jinx can't go snipe people at half health with her rocket and do 800 damage unless she builds for AD. Likewise, Trist can't E>AA>W>AA>R and instantly kill you unless she builds for AD. All AD and AAD would do as separate stats is force AD champs to choose how they want to play, and build for it. They wouldn't be good at everything anymore, and they'd have a real weakness depending on how they're building. As it is, tanks and bruisers build one or two AD items and the rest full tank, and then go and demolish entire teams. This system would prevent that, and make them a little more bearable.
What weakness does an ADC have? If you tell me they're squishy and easy to kill, I'm going to call BS, since I had a 6-man ult (5 people plus ghost) on Illaoi and used my W on an Ashe four times (and EVERY TENTACLE hit her), but she healed herself through it with nothing but a BT (I had 350 AD, so it was literally thousands of damage per W) -- she lived with like 30% health and then went on to kill another person before dying.