The problem with Anivia
I would like to start off, saying that
isn't as bad as other certain champions 
So, after playing a fair bit of
Through my league years, I see 3 problems with her.
•She is the most mana hungry champion I know •The range of her E is really short •The speed of her Q makes it easy to out run
so for those who don't know how
Works, if you slow someone with your Q or R your E will do double damage,
the problem with this is the range of her E,
•Lets say you manage to get a Q on a
who is running away, you move into range in order to get that Double damage with your E, he grabs you, spins, dunks you, you're dead cause your a Squishy mage,
but hey, you got that 600 dmg on him, now he has 75% of his hp left
•Lets say
ganks you, you manage to get the Q on him before he dashes, you get in range to E him, you get the E, he dashes to you, You Place down your R, both of y'all are now fighting in it, you then place down your W and use the wall to Juke him, he gets low, activates Undying rage, by this time your skills are on cool down, you stun him, it only last 1 second, he kills you, your passive is up though, your ult then goes down cause you ran out of mana, his attack speed is fast enough to kill your egg, you die
If you don't get what I'm trying to say, is that in order to cast your E, your are in a very dangerous zone, because you are so close to them, so anyone can just go ham on you, tearing you apart, the way to fix this is just increase the range of it by a bit, more similar to
's Q or
's Q, it would be much of a problem, but
is a mage, so she is squishy, and her only escape is a wall, someone can just flash/dash/teleport/jump over so you up the range of her E, she can still do the same dmg, she's still squishy, still has no good escape, but doesn't die in every team fight, just because she wants to Q then E someone
Now To address the Speed of her Q, when playing mid and Legend of the Poro king as
I noticed that the speed of her Q is about the same as a champion without boots, in fact even a champion with
can easily out run her Q, and not to mention champions with even the smallest dash, like
for example, and on occasion I've had
dash to a minion to dodge my Q, and you might say "well that's just cause they're good at dodging" but that's the thing with it, the projectile is so slow you don't need a good reaction time to dodge it, I have the reaction time of a ROCK and can manage to dodge it
so over all, the best way to fix
is to buff the speed of her Q by a bit,
buff the range of her E by a bit,
either give her more Mana regen, or decrease her mana costs
TL:DR her Q is slow and her E is too short of a range, and she's mana hungry, just buff her a bit and her problem is fixed.
and that's only the ones I remember seeing a lot
but I have only ever seen