I love playing Anivia, I do it all the time. She's got a good kit and is really fun to play as. Yeah she's super mana hungry especially early and mid game, and her Q is really slow, but I can't even count how many times the stun has saved me and my team. Her wall is difficult to use properly most of the time, but works wonders when used correctly. Her E is nice when you can set up a combo, and her R is a beast at clearing minion waves and in teamfights.
Overall I think Anivia is deserving of her maximum skill rank, and it's part of why I take pride in playing her well. The only thing I'd change about her is an increase to either her movement speed (She's among the slowest champs) or a slight increase to her Q projectile speed. This would just be to reward the skill of a player who plays Anivia well.
She's at the point where if she gets nerfed at all she'll become unplayable, but if she's boosted too much she'd become overpowered.