I was told anivia is a very high skill cap.

Watch some high level play of her. I've seen some cool plays with using wall to interrupt dashes, trap people against a wall and get a kill/force flash, or knock people into getting stunned by your ice ball.

Play her for yourself. If you climb out of silver she has low skill cap. If not, then you got your answer.

"High skill cap" is a fancy term for "takes 10 minutes to learn instead of 5"