Because the problem ISNT that shes untargetable and cant be damaged by AoE onces shes tethered; thats her major gameplay gimmick. With that in mind what is the problem with Yuumi, at least according to boards in the evening?
"Wahhhh I can't kill her"
Thats literally it. Shes a subpar character built around the concept of being last to die, which is frustrating to deal with. AFAIK she has never had a 50%+ winrate but people keep crying.
The biggest deal with her is the fact she can ride divers into battle. Zilean +Darius, darius will eventually leave him behind. Darius + Yuumi they go together.
Because the problem ISNT that shes untargetable and cant be damaged by AoE onces shes tethered
You cant just say it isnt a problem because you say so lol. It's a huge issue with her kit. You do not get to interact with her unless she lets you. She also has the hands down lowest skill floor in the game because of it
Yuumi's core issue is lack of interaction.
The main way for the enemy to interact with her is buying GW. That kinda says something.
The problem people have playing against her is absolutely her ability to become untargetable. When you think about it, all that it is really doing is forcing you to kill the ADC/host and keeping you from hurting the support. The issue is that she plays super safe and can get away very easily if other allies are around. I'd argue she lacks any survivability without allies and can also be one shot by basically anyone who builds damage or combo'd to death if she is hit by CC. She also can't roam effectively and unlike other enchanters needs to be attached to allies in order to heal/buff them.
So basically Yuumi players who know which characters to buff and when are going to be much stronger than ones who don't. Yuumi can turn the tide of any fight, within reason, if she is played properly. I also cannot count how many times people have died in a 2v1 with me on my ADC fighting as if I'm not there and then inevitably dying because they underestimated Yuumi's utility, she is not a glorified item. However, if you CC the character Yuumi is attached to she is either stuck there or needs to detach to try to float away with her 330 movement speed lol. I think Yuumi loses plenty of 2v2s.
She is by no means perfectly balanced but I don't think she is SUPER OP or COMPLETE GARBO. She should be balanced around the fact that she is untargetable most of the time tho, its still a very strong mechanic. I think as long as she doesn't do a lot of damage/has more reasons to detach or become vulnerable she should feel less annoying to play against.
Existing
She can sit on top of her ADC for an indefinite amount of time and spam abilities, and her entire kit revolves around her being attached to someone. The core of her design makes her harder to balance and it also creates scenarios that balancing with simple number changes can't fix. I've read posts that Yuumi promotes duo boosting cause a high rank adc will have an easier time carrying a Yuumi player. Its an uncommon scenario but Yuumi allows it to happen.
She doesn't need to build boots because she rarely detaches from allies except when they're dead. Though she can still build them I rarely see Yuumi players do it. Its a reasonable trade-off but it also means an extra 900-1100G to use for other items.
Because of how she's designed she can skip using flash as well. 
Imagine how strong any other support would be if they could stop using flash and start using Ignite and Exhaust instead? Her ADC can reliably use 
or 
instead of 
and Yuumi can use or or . It's also worth noting that Yuumi was able to teleport with allies she's attached to and Riot's removing that interaction because its too strong.
Now lets go off topic a little and remind you how hated and still hated 
meta was. People hated it so much that it that it got all enchanters nerfed and people are still mad about it and want supports to nerfed into the ground, but then they created this thing, the most uninteractive enchanter that may ever exist 
, so its not surprising that people hate laning against Yuumi.
The problem with her is that she is heavily reliant on your ADC or at least one of your team members being competent enough to know when to go in and when not to go in. That is the problem with her WINRATE. Same as Kalista. You cant just pick her up into a ranked game without being duoed with the adc, because often times they will start trolling no matter if you are a good yuumi or not. They will instantly assume that yuumi is a troll and so they will troll.
She isnt really PROBLEMATIC for those who have a clue how to play against her though, because the main thing is that you need team mates that will actually build a grevious item, and preferably have some way of locking down a single target. Leona, Naut, Thresh, Blitz.... Hard engage champs on a single target that will be played into yuumi. If your adc is not a Sivir or Ezreal that knows how to not be hooked, Yuumi will pretty much be a hard loss. If the adc is good, then she will bolster their skill with heals, speed, and additional damage, as well as a slow and aoe root.
So all in all, the main problem is that people A) pick her thinking its a free win and easy support. It isnt and she is not. and B) people do not know how to play against her, so she "feels oppressive".
Simply and in kind words, the majority of her abilities are frustrating to deal with because of the lack of counterplay. Now, they are testing stuff on the PBE to address these problems.
I want to question to the OP then. If being "unique" to the game is so crucial. Why was Nunu Karthus double jungle or taric Yi funnel not a thing anymore?
I don't know why people are so pissy about Yuumi Q. It only does damage if it can empower, and it doesn't even do that much. Plus it's a slow, single target, projectile that can be body blocked. You might as well be upset that Fiddlesticks is chipping you down with his crows, or that Xerath keeps blasting you from 1000 units away with his zap.
Pick someone with hard engage, and then shit on Yuumi. Especially early on in lane. Leona, Blitzcrank, Pyke, Nautilus, Thresh, etc. Not crushing Yuumi in lane is like not crushing Sona. You have only yourself to blame for allowing her to scale up into her AP hyper carry status.
Even worse, there is literally fuck all Yuumi can do to peel or protect her ADC against assassins. Zed, Talon, Fizz, Katarina, Leblanc, etc. They'll kill the ADC, and the they'll kill her too if no one else is near enough for her to jump to.
I think your premise is flawed. Just because her untargetability is her "major gameplay gimmick" doesn't mean that this gimmick couldn't turn out as problematic and unhealthy.
Anyway, there are also other aspects in her design. Her Q as a spell is virtually impossible to dodge if coordinated correctly, since she also has the unique gameplay gimmick that she is able to curve this spell mid flight. Then she also grants her host additional AD or AP based on her own and also gets a bonus from their stats herself. While this is fine in most situations, there also happen combinations which are kinda insane. Like a combination of Veigar and Yuumi, I had a game in which Yuumi then was able to oneshot squishies with her Q, thanks to the AP she got from her host.
I think the changes Riot are trying out for her now are pretty good. Taking some time away from Q means that it could become easier to dodge this skill (finally). And taking away charges from her heal makes her healing more bursty and less sustained, which I think is a plus.
The Problem is most often times whats behind the Keyboard.
Biggest issue with Yuumi is the untargetability.
It removes most of the need for her to interact in a lane.
If a Soraka or Sona misplays, they die. If a Yuumi misplays. HURR I PRESS W AND YOU CANT TOUCH ME ANYMORE.
Just because a champ is designed around a gimmick doesnt mean that gimmick is healthy. A perfect example of this is sylas, Look how hard his R (his "ult stealing gimmick") has had to be nerfed, He used to be able to steal enemy ults from 2 screens away and at level 16 ult twice in a teamfight, this was not shockingly blatantly imbalanced and he had to be nerfed heavily.
Historically for the enchanter class (which yuumi is undeniably one of) positioning has been an important factor, if a 
step up too far in lane and you risk getting clapped. Yuumi gets a free pass around these situations, and good yuumi's can even temporarily detach to block damage to their ally basically adding even more effective health on top of her shields/heals.
