Maybe I've been gone too long from the game and mabe I'm not skilled enough for my words to have much weight in this matter, but I bought Yuumi and gave her a try and I honestly don't think she belongs in the game.
Yuumi is supposed to be a support champion. She cannot be anything other than a support champion. Her kit simply and blatantly does not allow her to be played in any other role. This, in itself, is not necessarily a bad thing. She is not alone in this regard, after all.
That being said, however, what makes a good support?
A good support, in my opinion, needs to excel in four aspects. Presence, peel, awareness, and coordination.
Yuumi has no presence. If she's attached to an ally, usually the ADC, she provides almost nothing with the exception of some minor heals and the occasional tickle. If she is not attached, her allies gain no benefits from her abilities, and she's killed faster than a Soraka caught out in the enemy jungle.
Yuumi has no peel. She's basically a spectator who watches her allies, the friends she's supposed to be protecting die one by one, hopping from one sinking ship to another until she's run out of emergency exits and is slapped in the face with a well deserved death.
Yuumi is extraordinarily limited in providing awareness. While she can ward and attempt to destroy enemy wards, she usually must do so while unattached and vulnerable. While it is every player's responsibility to provide vision for the team, it is NOT their responsibility to act as a taxi to their support so as to plant wards.
While Yuumi following the every movement of an ally may seem like coordination at first, it is not. The reality of the situation is Yuumi is a crippled cat wholly incapable of walking on her own feet so that she has to piggyback on others both figuratively and literally and hope her allies can carry her to victory. She is dead weight to any team whose misfortune it is to suffer her presence.