The fundamental problems with poppy's kit right now is the fact that she's pretty much 100% feast or famine until you achieve her lategame power, at this point she can safely dive into the enemy team with her ultimate to kill priority targets. Early game she's not much fun to play since you can get bullied by a lot of other champions, especially if the player isn't experienced with her, and late game she isn't fun to fight against because of the aforementioned problem of the lack of interaction between her and her opponents.
In a way she's similar to the way Olaf worked before his nerfs, being able to leap into teams to murder someone, except that her ultimate blocks damage as well as cc that's coming from sources other than her target, and if she doesn't want her potential victim to be able to fight back she can ult a different target instead. I think that with a rework she could have her early/lategame strength disparity balanced out so she could feel rewarding at ever stage, as well as having a kit that feels more entertaining to play.