Counterplay is not a substitute for balance.
This is directed both at Riot and the boards at large. The existence of a contrary play pattern does not make a champion balanced.
Take, for example, Dr. Mundo, when he was out of control during Season 4. He was out of control because Spirit Visage and a specific mastery were synergizing too well with his ultimate, making him unkillable. Of course, counterplay did arise -- dive him pre-6, make sure to have Ignite, play Trundle, etc. -- but Mundo still needed a nerf. Despite the existence of counterplay, despite Mundo's not being a "guaranteed" win, he still deserved a nerf.
Some champions have very distinct play patterns that, when connecting properly, will win. This forces other champions to play around them. A good example is Blitzcrank. Blitzcrank is not overpowered, but he forces champions to play more carefully in lane, and later to be more careful about picks. His lane presence is balanced with mana cost and his late game potential is balanced with a strong front line.
Another good example is Malzahar. Malzahar has a very distinct playstyle, and if you're against a Malzahar, you know certain things about how you have to play. Post-6, he's going to attempt to use his ult while you're standing in his pool with space aids and his pet is attacking you. You can avoid dying by keeping yourself at or near full health and never putting yourself in a position to have all of that used on you (don't get too close, stay the HELL away from the space aids and from him when you HAVE the space aids, etc.). You can expect he'll win lane a little, but that's fine, because if he's not super fed, most mid lanes will have more impact on teamfights than Malz will. Thus, Malz, while possessing a distinct, often overbearing playstyle, is fairly well-balanced.
But what if he wasn't? What if Malzahar didn't need to line anything up or catch you at low health? What if you were up 1-0 and 20 cs vs a Malz, you were full health and had an MR item, and he hit 6, moved forward and used his E and R combo, plus ignite, and killed you. No Q or W, no voidling, no minion damage, just a quick use of his ult and highest level ability. As the last tick of ignite is killing you, he's already walking away typing "#rekt" in all chat.
He would still have windows to exploit. You'd still be able to play against him pretty much the same way, with regards to focusing on avoidance and trying to stay alive, with the expectation that your 5v5 impact would be greater than his. Despite the existing counterplay, however, he would STILL be overpowered.
Another example. Let's say you're playing Jayce in top lane against a melee champ (awesome, right?). You go to town with the harass. The enemy champ can't get a cs. More, the enemy champ is playing poorly. They're getting frustrated and missing skillshots, taking way too much damage trying to get a minion... eventually they're at 1/3 health and you go in for the kill. Get it. First Blood. Awesome. You do this two more times.
Now you're in lane again, and it's the same deal -- harassing the hell out of this champ. You just came back to lane with BF Sword, to go with the Sheen you already purchased. You're at level 9 to their 6. Again, you harass the enemy down. Now they're at 1/2 health. You land another accelerated Shock Blast, hitting them and removing several of their minions, and you go in.
You are killed. Just evaporated. Your combo lands and takes the enemy sub-200 health, but the enemy's combo, including ult, lands, you die and they don't. You say "what the hell?" and tab to see what the enemy champ has. They have a Doran's Shield, Ruby Crystal and a Longsword -- the components to Phage -- and Boots.
To recap, you were up three levels, you had a BF Sword and Sheen to their Longsword, Doran's Shield and Ruby Crystal, and they were at 1/2 health to your near-full health (you've taken damage from creeps when autoing the enemy). They were actually below 1/2 health when you engaged because you landed your Shock Blast, and the minions were mostly dead so it's not like they were a large factor.
This example happened. It sounds ridiculous -- it IS ridiculous -- but it happened. If you had to guess, what champion would you say it happened against?
That's right, it was Illaoi.
Now, I agree with everyone that counterpicks exist. That Illaoi can be kited. That Illaoi's play pattern is largely about getting close to you. One could easily say, "well, by engaging Illaoi directly, you were playing into her hands." And you're sort of right.
That said, how much power is her play pattern supposed to be worth? Obviously, with two champions at equal experience and build, Illaoi is going to have the advantage up close, because that's her strength. Also obviously, a level 1, zero-item Illaoi will lose to a level 13, half-build Soraka, even up close, in her element. The play pattern is worth only a portion of the power gap.
This runs both ways. If Illaoi is level 12, and is playing against a level 5 Vayne, she will NOT expect to be kited to oblivion, even though Vayne as a champion has the tools to do it. Illaoi can expect that Vayne will not be a significant threat to her, because the power discrepancy is large enough to outweigh the favorable play pattern.
So we again return to the question -- how much power is her play pattern worth? If Jayce has Essence Reaver and Infinity Edge, and engages up close on a full health Illaoi with only a Doran's Shield, and the Jayce has a 5-level advantage, who do you expect to win the fight? What if it's only a four-level advantage? What if the Infinity Edge is only a BF Sword and a Cloak of Agility? At what point do you say, "yes, Illaoi should rightfully win there -- she's behind, but still excels up close?"
My point is that the place that SHOULD be and the place it IS are in two different spots. Illaoi can still be outplayed. She can still be countered. You can still successfully avoid her play pattern. Still, we have to go back to the original point: counterplay is not a substitute for balance. There are several factors in play when you engage a champion -- health, mana, levels, items, minion count, the presence of a turret, close quarters or ranged fight, etc. -- and when only ONE of those factors is in a champion's favor, with all other factors being either equal or heavily in the opponent's favor, that champion SHOULD NOT WIN.
Otherwise, the champion is unbalanced, and no amount of counterplay will change that.
EDIT: For everyone who says "well, that's to be expected," I again emphasize this question: At what point is it expected that a Jayce could kill a full-health Illaoi at close range? I know that Illaoi excels at close range, but do you believe that, say, a level 18 Jayce with full build should lose to a level 6 Illaoi with no items? If you believe that, then clearly there's something wrong with Illaoi, as you couldn't say that with ANY other champion. If you agree that once Jayce is level 18 and has full build, he should be able to beat an Illaoi in close quarters, then we have to figure out where the line should be.
A 12-level, 6-item advantage is enough? Okay, how about a 10-level, 5-item advantage? How about a 6-level, 3-item advantage?
Once you have that figured out, you're essentially saying, "Illaoi's strength in close quarters is worth X amount of levels and Y amount of items." When you figure that out, you have to decide, "Is that value balanced?" The question has NEVER been whether Illaoi is possible to defeat, the question is whether her strength is greater than it should be.
And one final thought -- I recently played a game where I was on the same team with an Illaoi support. This support took no farm in lane and their lane actually got pretty well stomped. I was carrying hard from the top lane, and then I did a stupid thing in the mid-late game and got picked off and killed. I figured we were in trouble, but my team engaged the other team at Baron 3v5. The Illaoi got a quadra kill. I looked at her items -- she had the new sightstone/runic shield item, a Black Cleaver and a Warden's Mail. True, the enemy team was grouped up, and had been taking damage from Baron, but she came out of nowhere to carry the team there. Name for me another champion who can do that. Even Annie is going "wait, WHAT?"