So.. the text got a bit longer than intended, but whatever.
Sorry, but... "strong, strong early game"? What? Ahris early game is anything but strong. She has a rather low damage and quite high manacosts; if you die to Ahri pre lvl 6 you fucked up, and you fucked up big by getting poked down by multiple Q's and then misspositioning and eating a charm. And even with 6 she will not just jump on you and 100-0 you. Even with ignite she simply doesn't have the damage to do that. Especially if you invest the 720 gold for an early negatron cloak.
"Tankbuster"? WTF? Vayne is a tankbuster, Fiora can kill tanks quickly. Ahri doesn't become a tankbuster just because half (!) the dmg of her Q is true dmg. If one half of her spells having true dmg is enough for being labeled "tankbuster" then Olaf, Rek'sai and whoever has any true dmg is a tankbuster too...
Tanks are not only about resistances, but it comes with health, and the bit of true dmg doesn't do anything to that.
"Best single target CC of the game"? Really? It's a 12second, single-target, blockable Spell, with a duration of 1/1,25/1,5/1,75/2 seconds, and since basically everyone levels charm last, you will only be charmed for 1s for most of the game. Twisted Fates gold card stuns for the same duration, on half the cooldown and is targeted. Morgana can root you for 2-3 seconds.
Sustained dmg, she has, yes, if you go for 45% CDR, then you can rotate your spells rather quickly. Burst of an Assassin? Her second Class is Assassin, so one would guess its reasonable to have some burst dmg. Although her burst is certainly not on the same level of other AP-Assassins; Leblanc, Fizz, Diana (not considered an Assassin by Riot but she feels like one). A 6 Item Ahri will of course oneshot a very squishy target with a full combo, but that goes for basically all champs. Her dmg is not the best in either category; there are other mages who have better sustained damage on higher range, and there are other champs who have better burst. (Ever been oneshot by a lux-combo out of fog of war from half a screen away?^^)
"Good poke"? The only real poke is her Q, and it's a decent poke tool. Nothing special, though; champs like Xerath, Lux or Ziggs have good poke, thats easier to hit with a longer range.
"sustain"? Yeah, with the conditions that she needs to hit 9 targets before it activates+ another spell, where she heals for the number of targets, so atleast 3 spells casted to get the sustain. And then it's after the nerfs last year not even that strong. It's something nice to have that helps her a bit trough laning-phase, but you can't just spam spells to get the heal. Unless you want to burn through your manapool very, very quick.
With all due respect: You are vastly overexaggerating basically everything about her.
So, her weaknesses: Opposite to your claims, she has a vulnerable early-game. She has high manacosts, so she has to be very conservative with her mana. Even just showing up as a jungler and getting her to burn mana on a charm+q to get away will hurt her, because now her manabar is depleted and the lane control is up to you.
She is extremely heavily ult-reliant. Ahri without her ult is a lot less dangerous than with it; unlike other champs like Leblanc or Fizz she has no rather low CD gapclosers on her basic abilitys. You need to make use of that.
(And on a side note, shes squishy as hell; catch her with a single CC and she gets blown up; and since her ult are dashes not blinks or flashes, you can even hit her mid-Ult. But being squishy goes for other champions aswell, so just a side-note)
Her greatest strength is that she is indeed able to do something of anything in some way. You are right in that way, she has basically anything to some degree; just not nearly to the degree you are making it out to be. She is decent-good in most things, but she is not the best in any category. Not the best dmg in the game, not the best permanent mobility in the game (as its tied to her ult, not on a rather low CD basic ability), not the best CC in the game (not even singe-target, let alone speaking about AOE-CC), not the best poke, not the best sustain, and please never call her a tankbuster again ._.
It however makes her a very safe champ, who is, if you know how, able to adapt to basically every matchup and somehow stay relevant. Shes not a pure feast or famine champ that needs to win lane hard, and thats why she is quite good in a solo environment. She doesn't have alot "You are to autolose this matchup", since you have the "outplay"-potential with your ult in almost every matchup. Aside from maybe Leblanc; I think it was in the C9Challenger vs NRG yesterday at the promotion-Tournament where it was Hai on Leblanc and he dumpstered GBM on Ahri. But it requires you to be somewhat good at Leblanc and playing her correctly, so it might not always happen in lower Elos.^^
More important: Even if you lose lane, you can stay rather safe and don't feed. Thats in my opinion the biggest reason for her high winrate; even if you lose, you won't necessarily feed 5+ kills to the enemy midlaner, thus making it easier to comeback for the rest of the team. If a Yasuo loses lane, he usually loses hard and when the 5/0/0 Midlaner then shows up Botlane things get rough...
On the other hand, Ahri doesn't really have any matchups where she autowins by default. Twisted Fate, okay, but everyone is supposed to win lane in a pure 1v1 against TF. It all comes down to how good you are and how good your enemy is. If you on your champ are really better that the enemy Ahri, you have a good chance to win. If the enemy Ahri is better then you, then she has a very good chance to win. Basically, I feel like Ahri has the ability to turn most matchups in skill-matchups; who can hit his skillshots better, who handels the lane better, jungle pressure, playing around enemy cooldowns etc.
All together make her a very good champion in the more chaotic Solo-Environment and thats why she has a quite high winrate there. In high-Elo (talking Master-Challenger-ProPlay) however she is basically not seen; yeah yeah, as mentioned she was played by GBM yesterday but that was purely because its a comfort-pick, not because shes a strong pick. In the 4 big regions (EU, NA, China, Korea) she was in this summer split played exactly THREE times. Once again by GBM (lost), once by Ian from MVP in Korea (lost) and once by We1less in China (won, but that match had no effect for the standings and the enemy team played with Urgot ADC...^^) She just doesn't offer anything special. If you want Waveclear and AOE dmg, get Viktor. If you want high CC, get Lissandra. If you want lategame teamfighting, get Vladimir. You want great roams, get Taliyah. You want a strong AP-Assasin? Get Leblanc (for the early snowball) or Kassadin (for the late game). You want Utility? Get Zilean or Karma. A midlane Hyper-Carry? Azir (pre-his latest nerfs) or Cassiopeia.
I wouldn't be suprised if Ahri gets a nerf due to her Solo-Q Performance in the nearer future, once they have finished with the Balance changes for worlds. But yeah. You overplay her strenghts to an extreme and completely unjustified degree. I mean... tankbuster. Come on D:
