(Sorry I put up the wrong version by accident but all should be fixed now).
Anivia is a champion that has been appearing a little more in the competitive realm as a situational pick. The biggest reason for her appearance is her ability to kite her opponents. Her kit also allows her to zone enemy champions out from fights and create divides between champions. In terms of becoming a power pick Anivia has not been able to hit the mark. There are a few different reasons for this but not all are negative reasons. For the best understanding you have to look at her strengths before her weaknesses.
Before we get into it I have information to show scaling and example compositions that Anivia has appeared in.
Composition Examples (Origen vs Flash Wolves)
Anivia does well in compositions that want to peel, kite, and slow their opponents as seen in the Origen compositions. This is because of her natural ability to kite champions since her kit is all about control. Glacial Storm and Frost Bolt can slow down multiple enemies at once since both are area of effect spells. The slow from Frost Bolt lasts three seconds while the Glacial Storm’s slows stay for its duration. Anivia’s slows are quite powerful because they take away 20 percent move speed while dealing damage. In addition to Glacial Storm’s move speed slow it also lowers the enemies’ attack speed by 20 percent so marksman or other attack speed heavy champions put out less damage in a fight if they are in the storm. Then you combine all the slow effects from those spells with the wall from Crystallize enemies become forced to walk through certain areas or they get blocked off. Frost Bolt also has a one second stun on the second activation so she can trade when enemies do try to jump on her. If the Anivia is quick enough with Frost Bolt she can use it to stun enemies that try to immediately jump onto her so she can get away. The stun can also be used on enemies walking through Glacial Storm to stack on more damage and to keep them in the storm. All of these spells combined create an area of zone control for Anivia and her teammates to fight under less pressure.
Anivia’s kite potential is quite punishing with her utility however her damage is nothing to mock either. If you look at her scaling on Frost Bolt and Frostbite both scale with 50 percent of her ability power. At first it seems fairly low but Anivia can chain Frost Bolt damage and Frostbite gets amplified when an enemy is chilled. Frost Bolt can hit a target with both activations so you do double damage. If you can manage to hit both activations while the opponent is chilled and stunned you combo with Frostbite it gets damage doubled as well. This combo can force enemies into early backs and it can give Anivia free time to farm depending on how much health the enemy lost. Glacial Storm can also be used to get double damage on Frostbite without having to rely on Frost Bolt as well however this combo does open up for your opponent to trade back if you don’t use Frost Bolt. If you are feeling risky you can use Crystallize to try and force an all in fight by cutting off your opponents escape. Her Frost Bolt and Glacial Storm also make for good wave clear to stop sieges since they can hit all the minions and kill fairly fast. This can put the enemy team in a position where they might try to dive or force them to back off and wait for a fight at an objective.
The last thing I’ll mention is Anivia’s core build path that scales well into the late game since it consists of Archangel’s Staff, Rod of Ages, and Ionian Boots. Both of Archangel’s and RoA synergize well since RoA grants ability power, health, and mana over time and the mana scaling helps Archangel’s since Archangel’s gives ability power based on a percent of Anivia’s total mana pool. Ionian Boots help to make up from missing Cooldown Reduction since she does not pick up Athene’s or Nomicon in this build path. The rest of Anivia’s build path also tends to be quite flexible after her core since she has the ability to kite combined with the extra health and shield from her build. This means she can go straight for Deathcap, Liandry’s, or Hourglass depending on the situation or whatever the player values at the time.
There is a reason I went over Anivia’s strengths before going into her weaknesses in competitive. The reason Anivia is not a power pick is that Anivia’s strengths are her weaknesses. It’s definitely weird to read at first but once you think about it you will understand.
Anivia has a base move speed of 325 but this isn’t the only issues but it does play a factor in them. Anivia’s kit is all about punishing her enemies for being aggressive but the issue being her kit makes her reactivate leaving few ways of forcing aggression herself especially early on. If Anivia wants to effectively trade she always has to combo abilities since Frostbite doesn’t do double damage on their own. This takes quite the toll on Anivia’s mana pool since a Frost Bolt into Frostbite combo is 130 mana at level two. You also have to factor in how slow Frost Bolt moves combined with Anivia slow speed and it can make trades hard which is why you also see abilities like Crystallize used to help trading by forcing the enemy into the Frost Bolt. A three spell combo like that takes 200 mana at level 3 if you have a point in each ability slot. Depending on the situation of the lane match up at level four it can take anywhere between 150 mana if have two point in both Frost moves or up to 210 mana with another point in Frost Bolt and a point in the other two. It does get easier when Glacial Storm is available but it drains through mana quite fast even if it’s only on for a few seconds. Not only that you are still open to being counter traded if you don’t use Frost Bolt in the combo of spells. Meanwhile there are champions like Viktor that aren’t required to constantly combo abilities to get solid trades. Champions that can trade more freely get an easier lane against Anivia since her aggression is telegraphed since her trade is all about the combo of abilities.
Then Anivia’s core build path is strong late game but it does have problems early on. It requires a lot of time to scale since RoA still needs ten minutes to charge up and Tear needs ability casts to stack which takes a lot of time. This is why you hear Anivia players talk about giving up lane phase early because you don’t build any damage and most of your build early on only affects Anivia’s mana pool. The build takes a long time to get into relevance it isn’t until 20 minutes before she starts hitting that power spike. If Anivia is unable to go this high scaling route she actually suffers a lot since her mana pool will be significantly smaller with something like Athene’s instead of Tear. The smaller mana pool also means she gets less attempts to trade, less spell spamming, and her Glacial Storm can’t stay up as long in drawn out fights. Athene’s does give an early power spike but it’s no longer as strong since the changes to RoA and Tear.
It’s these strengths and weakness that put Anivia in a position where she is only strong in kite/peel compositions. Her ability to punish enemies for approaching her and her ability to clear waves during sieges is quite strong but she gives up a lot to be good at it. Being Aggressive is quite hard for Anivia because her kit is all about kiting but in those kite and peel scenarios she doesn’t half to be aggressive. She can wait for the enemy team to start a fight and work on keeping her teammates alive while trading damage. Her team can also make up for weaknesses by taking picks like Sivir or Alistar that offer more move speed, additional peel, or engage.
For Anivia to ever be a contested power pick she would probably need changes to her kit but at the same time I don’t think she needs them. There are already aggressive characters like Viktor, Azir, Yasuo, or Twisted Fate that can be chosen. Anivia brings a unique style of play to the mid lane with weird build paths and being able to change half the battle field with Crystallize and Glacial Storm. There are not many characters that play team fights like Anivia which just adds to this new unique style she can bring towards the game.