I don't feel like getting too much into why I think Yuumi is weak as it's not the point of this post, but long story short she has a negligible lane presence and doesn't scale well into the lategame. I don't think that Yuumi being weak is a problem at all though, for several reasons:
1. Yuumi's kit is extremely fun to play, even if it is underpowered. Keeping a champion on a power level that is fun for both teams is a win-win scenario in my opinion.
2. Yuumi has some effects that would be extremely nasty to play against if she was stronger, notably her w.
3. Yuumi is an extremely niche champion. Her playstyle is very unique and is probably not as enjoyable to every player, so it would be rather bad for the playrate of the support role if she was a must-pick I think.
4. Yuumi requires your adc to adjust their playstyle, which not every adc may want to do. If Yuumi was more relevant it could force adcs into playstyles they do not enjoy (specifically agressive playstyles - Yuui can't do anything when you're towerhugging) or force them out of their role, which is not a good thing.
Also side note: Yuumi isn't all that complicated to play (although it can be a tad weird for your adc but eh), but she has a bit of a noob trap imo. She can't do anything without her passive but her passive doesn't have any noticeable indicator for when it's off cooldown, which results in newer Yuumi players underusing it. I think it should have a cd indicator/voice lines when it's up to make in crystal clear to players that they should be proccing that passive whenever they realisticly can. It would also be nice for it to explicitly mention that this effect does not get triggered by the attacks of whomever you're attached to, as that was most certainly confusing the first few Yuumi games I played.