Yuumi is just an awful concept (and the reasons why)
Yuumi as a champion simply isn't fair, even by DOTA 2 levels of insanity. Lifestealer is probably the closest thing to Yuumi in DOTA 2 and he doesn't heal, have a slow with the range of an entire lane, a better Sona ult, scaling damage bonuses, shields and did I mention healing? The most Naix (Lifestealer) can do is burst out of someone and be like "SURPRISE!", and that's that.
Oh, and did I mention that Lifestealer's parasitic ability is....wait for this.....AN ULTIMATE!
Yuumi's W is a basic ability that has basically no cooldown, and a very low punish window to actually stop her from doing what she needs to do (her travel speed is also far too high for you to catch, so yeah, that's a thing).
So, apart from this very clear comparison, what else makes Yuumi an irritation?
Well, for one she turns bot lane into a stalemate, until she starts spamming Qs and you start crying (which I'll get into below). When you play against Yuumi in the bot lane you just don't get to interact with your lane opponent (because Yuumi turns the lane into a pseudo juggernaut vs 2 people) because if you do you will lose due to Yuumi healing her ADC whenever you try to trade, which results in a loss as Yuumi will then go back to spamming Qs from inside her host.
Surely there's counterplay to this, right? Well, there is, but much like Yasuo aspects of her kit counter it out, which I'll get into now.
Yuumi's Q: Ok, so, Morg Q and Lux Q are bad, but that's only because of their hitbox. Yuumi's Q is a whole other level of stupid....
The fact that Yuumi can "guide" her Q from inside her host is already atrocious in terms of counterplay since upon missing the skillshot she can try again, and again....and again. However, that simply is not the end of the story here, as the Q itself lasts almost 2.5 seconds while in flight. So, what ends up happening is Yuumi misses the initial Q, then goes for the attempt 3-4 more times, even when you're sitting inside of creeps or teammates.
On top of these two aspects there also lies no window for punishes as she's sitting comfortably and safely inside of her host with the Q possessing the range of a Yasuo ult (which is a really large range by the way).
Side note, the Q does far too much damage (and has too much AP scaling) and the slow on it is quite large, so getting hit by it is definitely not something you can shrug off at any point in the game.
tl;dr, the three aspects of her Q that make it extremely unhealthy would be, the "guide" feature, the duration of the cast and the range of the Q; all on top of the fact she remains untargetable so that you can't actually stop the cast.
This ability definitely needs to be reworked/nerfed as it does not possess enough counterplay for such an impactful skillshot.
Yuumi's heal: Let me just get this point out of the way here, with that being, Grevious Wounds. It doesn't matter if you apply Grevious Wounds to her target, because 40% of ~560 is 224 (and that's from Kat's ultimate). 60% of that is 336. I'm pulling the figure of 560 from my experience playing both with and against Yuumis in the mid game.
Sure, early game, Grevious Wounds actually matter as her heal isn't too volatile in lane. However, the moment she picks up Ardent+Athene's GW are just an annoyance for Yuumi, she still does her job insanely well, and that's because of.....
The goddamn movement speed: As it turns out, Yuumi's heal doesn't just provide the obvious health, it also gives an insane boost of movement speed, which she can use twice, AND IT STACKS! This in of itself invalidates supports such as Lulu who provide the same movement speed, just without the healing and spam-ability of Yuumi's E.
The shield: Her passive is just a better Rakan passive that provides a shield for both members (in practice because of Yuumi being untargetable). The fact she has a shield on top of her healing, being untargetable and her insane ulti is beyond me. That said, at least she has to BRIEFLY exit her host to obtain it.
So, with all of that out of the way, what about when Yuumi's heal isn't under the effect of Grevious Wounds?
Well....it's a dumb amount. It's a better Sona heal (minus the auto shield on cast) that increases the lower HP you are, and she can have 2 of them at a time, and the cooldown of it in the mid game is basically non-existent, especially if you manage it like a Riven Q and delay your casts to have it up near indefinitely. Let me put it this way, if she uses BOTH stacks of her heal she can heal someone for close to 1.3k-1.4k post Ardent+Athene's when someone is even close to 50% HP. When someone is at ~75% it still heals for close to 700. That is without accounting for the shield provided by Aery (unless she's running Comet), as well as the movement speed.
Who knew such a simple ability would be so incredibly IMBA....
Yuumi's R: Better Sona ult with a lower cooldown, way longer range, more damage and she's untargetable while casting it. Sure, her target is targetable, but what if she's inside a tank what then? Or what if she's inside a champ that can go untargetable/invisible? The risk-reward ratio is skewed due to these other factors to consider.
So basically, you have a support that's untargetable, provides insane healing, movement speed, shields, insane poke damage that is incredibly hard to dodge, has a better Sona ult.....I'm sorry, but all I can say here is that she's so overloaded she outclasses other enchanter (or enchanter-esque champs), being: 
and 
.
The fact she outclasses every other champion like her just isn't fair as the only reason to pick any enchanter not named Yuumi is, wait for it.....DING DING DING, when she's banned!
With all of that said, what are some changes I'd suggest? Well, they would be:
-Revert the nerfs to her passive, so that she actually has some incentive to exit her host(s) -Lower her base HP and HP scaling so that she's almost insta-dead when outside of her host(s), as untargetability of this nature is unhealthy and shouldn't be so forgiving -Rework her Q, or nerf all of the above aspects of it outside of MAYBE the slow amount -Remove the movement speed buff from E -Decrease the mana cost on E, but lower the healing amount -Give her W a larger cooldown so that she can't just jump in and out of targets endlessly -Increase her R's cooldown, as well as the time it takes to root a target and decrease its range
Honestly, I'd rather her being removed from the game as opposed to her being changed, but hey, here are some changes that pretty much need to happen to ensure that bot lane is no longer just "Yuumi was picked so now the game is extremely boring and frustrating", as I'm personally sick of it, and I'm sure most players are as well.
Side note: Nerf Pyke and Lux as well, Lux, Pyke and Yuumi are all destroying bot lane. Thanks.
, I'm glad too see that there is one guy who actually fears to play against a Yuumi.
his E can interrupt Yuumi's W also his passive can still kill Yuumi when she jumps on someone.
his Q will still damage Yuumi even if she jumps on someone. also, he can place two Qs in Yuumi's jump path stunning her and interrupting her W, knowing the damage of Zilean this would most likely kill Yuumi.
he can pull Yuumi like Blitz and Thresh but they do it a lot better. His ult if placed on Yuumi can interrupt her W if it gets to her but if it doesn't it still damages her and whoever she jumps on.
like Darius's passive his poison can still kill her even if she jumps on someone, I'm also sure he can blind her passive too.