Elise won't fall off as hard if Cocoon's stun duration increase with R instead of E
I will introduce my point with some statistics.
Scroll down to the graph "Win Rate/Game Duration", and you can see that Elise's win rate drop by 15% as game length increases from 10 minutes (~55%) to 20 minutes (~40%). She fall from her strongest stage to her weakest stage within just 10 minutes. (Obviously games that finish before 10 minutes are rare and the sample size will be small, but compare the same stats for Lee Sin and Nidalee vs Amumu, Warwick, and Master Yi and you will see that it's legit. )
10-20 minutes roughly corresponds when champions are level 7-13, the period when they finish maxing their 1st ability and put points in their 2nd. Elise's 1st ability (Q) scale very well with levels and it's contributes to her solid early early game. However, there is no good option to max out her 2nd ability.
If she max W second, she will have no skirmish and teamfight presence:
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Utility: All she has is Cocoon, an extremely skinny skillshot that stuns just 1 person for 1 second, on a 14s cooldown (11 with 20% cdr). That's really underwhelming for a spell that you can only use once in most fights.
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Damage: Sounds good on paper, but Human W is unlikely to land on more than 1 target and scale with AP. Spider W is unlikely to be used to full potential because it requires her to be in middle of everyone for extended duration, a task she's too squishy carry out mid-game. _The only reliable benefits from W second is better clear and dueling. Even so, the increased dueling power doesn't make Elise an excellent mid game duelist, it merely makes her not a terrible duelist because she lacks an ultimate which are excellent tools in most cases. _
So how about E second?
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Utility: 2 second stun on 10s cooldown (8 with 20% cdr) isn't bad. Skillshot still hard to land but it will make an impact if you do, and you can use it twice in a fight with some CDR. This is why Cocoon Bot was a thing in competitive play before Cocoon was made narrower.
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**Damage: **What could go wrong by not maxing a damage ability second? Not only will she do less damage than a support in a skirmish (most of whom have an ultimate, and 2 damage dealing abilities maxed out), she will also have some of the worst clears in the game. Not good when you want those tank and CDR stats to be a good Cocoon Bot. Elise will be useful in skirmish and teamfights as a Cocoon Bot if she gets enough CDR and tank stats (live longer = more Cocoon), but she will unlikely get enough gold because she can't dish out enough damage to get kills, and she can't clear her own jungle very well either.
This is a reason (among many others) behind Elise falling off. She can choose to get enough utility to be relevant in fights, or enough clear to keep up in gold and experience, but she can't get both. She needs both to compensate for not having an ultimate. It's very easy to change this though:
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E - Cocoon Cooldown: 14/13/12/11/10 -> 10
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** R - Spider Form/Human Form** Cocoon stun duration: 1.25/1.5/1.75/2 seconds
Elise now gets all the benefits of upgraded Cocoon while maxing W second. Compared to current E 2nd Elise, Cocoon will be better prior to level 12 (rank 4 E), worse from 13-16, and same afterwards. The early game Cocoon buff may be a problem, but 0.25s isn't be game changing. 10s cooldown also isn't much of an improvement from 14s, she won't have much CDR that early and she can still only use it once in most ganks and fights.
This won't solve all of Elise's scaling problems, but it is small buff that will push her closer to viability. I'd much rather Riot buff her slowly and consistently like this.
**Tldr; Elise falls off so hard partially because she faces a lose-lose situation after level 9 in terms of what ability to max second. Shifting Cocoon scaling to her ultimate will allow her to receive most benefits from maxing both abilities. **