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Eve can do quite well if your team can support her and they are very good with the char. It can be hard to counter Eve ganking early game, either that or you end up spending a lot of gold on things you could have otherwise, so she is still very effective.
The reason she is so freakin counterable is the same reason any squishie damager is under powered which is also melee. They are squishie, and they are up close and can be shut down in the duration of a stun. All it takes is a stun and an oracles and even 22/0 fed eve is dead if you go pure damage.
If say.. veigar stuns said ppl though she can down 2 or 3 in the same stun time (if she's fed). So it comes down to team work. I'd rather have Eve than Yi, honestly. Yi is terribad. At least Evelyn can make them burn money on oracles. Really I think you have to mix survivability with Eve, Trynd (b/c he can still be killed in a stun and not get off his ult), Yi, Katarina, or anyone else of like make or they are a waste.