Can we make it possible for Anivia to fall behind?

I groan whenever I see that I am going to encounter Anivia in the mid lane, where she is mostly played. This lane is barely winnable, but it's not because of her damage. Even if you outplay her, there's very little chance you will actually gain an advantage over her because you are not rewarded gold unless you can also kill the egg. This is a huge problem because unless you or your jungler are playing a DPS champion (or LB) then the egg will deny you an advantage. Her passive, while not outright busted in terms of gameplay, gives her unnecessary padding that guarantees she won't fall behind in gold. She may have low HP, but at the same time she has no reason to put herself at risk. The issue is compounded by the fact that when she hits Lvl. 6 then she will have one of the best waveclears in the game and thus force you to focus on clearing her wave. When she finishes RoA, almost all opportunities to kill her will vanish until teams begin roaming.

I'm not saying that she will beat you in lane; I'm saying if you are a better player than the Anivia then it simply means you will break around even. Getting ahead takes an obscene amount of effort and resources. Fixing her AP ratios won't solve the problem.