Evelynn needs a rework

Note for lazy people: if you don't want to read the reasons why I believe Evelynn needs a rework, you can still read my 2nd post which shows how she could be reworked.

Hello, I've been playing Evelynn for a while now, I love this champion but over time I could see many thing wrong on this champion's design that makes playing her really frustrating. I really believe that she needs a rework and I will give some rework ideas at the end of this post. (Don't debate on values because they are indicative and obviously need to be balanced).

1. Evelynn is made to punish enemy's bad move, to force enemies to be very careful because she can be potentially everywhere (if you don't have sigh on her, meaning that warding her jungle camps helps a lot). Howether, she is a very bad duellist and being a jungler gives her an xp disadvantage on solo laners. In the end, most solo laners don't care about evelynn and can actually do some very aggressive moves (like staying on their lane midlife and pushing or proxying) because they either: have enough damage to 100-0 her before she has done anything to them, have a strong enough escape/hard cc to get away from her or they are too tanky so they can just walk back to their turret. What should be her main strength(pressuring enemy team) doesn't work on most solo laners. Her fragility and her low base damage makes her one of the easiest jungler to get a double kill on when she is ganking.

2. Her skillset is designed for teamfights whereas her gameplay totally hates teamfight. Teamfighting and fair fights are the worst thing that can happen when you are playing Evelynn: all her gameplay is based on taking advantage of your stealth to catch enemies one by one or to surprise enemies by your presence. The best counter to evelynn is to actually group and force a fight because she needs to set up her actions, to flank enemy team to reach important targets, she cannot just go in. In teamfight, it's way harder to reach carries and going in mostly means that you get focused and killed because you neither have a decent burst to kill a target and get away fast, neither have a decent dps and tankiness to stay long enough in the fight to kill carries. Howether, her Q deals AoE damage, her W's CD is reduced for each enemy hit by her Q, her ult gives her a shield based on the number of enemies hit. Her spells give her tools for situations that she doesn't want to happen and are never enough. If you can hit 5 enemies with your ult, you die anyway because you are focused by 5 people.

3. Her skillset is kinda boring and she doesn't have much outplay potential, that's all about numbers, once you have engaged a fight, there is nothing else to do than hopping that you have enough damage to kill, enough ms to chase. Okay maybe the only thing is to think about is to keep your W to remove slows.

4. Her E and R don't fit with her gameplay. Her E gives an AS boost whereas you mostly play her AP meaning that it's totally useless because her attacks deal almost no damage.

Her ult, because it shields based on the number of enemies hit and deals damages based on the target current's health whereas her gameplay is very opportunistic and your goal isn't to catch full life Sion, Leona and Sejuani warding their jungle but to punish squishy targets when they are out of position. As her only CC and defensive skill she needs it very often but it has 150s CD, meaning the same as Amumu's/Nocturne'ult... If you want to outplay your enemy and shield yourself at the last moment, your ult deals 0 damage. If you want to keep your slow for when your target uses his escape, your ult deals 0 damage.

I understand that nobody wants Evelynn coming out from stealth and one shooting them like Rengar but giving damage based on her target's current health totally ruins her gameplay. That's why I believe that her skillset needs to be updated to enforce her strength: catching and chasing enemies out of position, giving her tools for that kind of situations instead of the patchwork that she actually is.