As a 1 mil Anivia main, i can say her passive is my favorite skill in the whole game.
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That passive is your free ticket to aggress on enemies, it isn't just a survival tool. Making use of it all depends on your knowledge of Anivia and the game in general. Really hard to make use of, yes, but hardly worthless.
exactly, Playing Anivia means knowing when you can go aggressive and when you should not. For instance, if their Jungler is nearby, then even your egg will not save you. however if it is just the 1v1 and they go all in your egg will save you from a death and you have the possibility of killing them if they stick around too long