To be honest, Zoe's characterization is atrocious
It boils down to the cosmic fuckup that is giving a lazy, willful brat immense temporal and magical power.
Zoe's biography describes her in no uncertain terms as a lazy student who mocks her teachers and treats her studies like a joke. With no other context, such as the actual nature of the studies or how her teachers treat her, this is an immediate red flag. Anyone in any profession ever has immediate cause to just dislike Zoe from the start. My father used to work as a drama teacher and my mother is a clinical psychology professor; they didn't suffer students like this and would often complain about them at home and how they only make their jobs harder. Anyone who has ever been a student ever can also totally appreciate this - you may dislike school, or be uninterested in your studies, but that doesn't mean you should go out of your way to antagonize your teachers, so long as they aren't doing the same to you. If you behave like this, then you're a spoiled brat. Even worse, you're a lazy brat. Everything in Zoe's biography and color piece point to her having no socialization skills whatsoever and the tact of something decidedly more sinister than she should be. Do we have villainous champions who are a thousand times more despicable than Zoe? Of course. She pales in comparison to Swain, Mordekaiser, Vel'Koz, and Tahm Kench. The difference is that Zoe is protrayed as a cutesy kid who doesn't know any better, when in reality her total incompetence and refusal to hold herself to any form of self-agency is being passed over as XD so random sparkles! preteen idiosyncracies. This is a total break from the internal standards I thought Riot held their characters to.
What the hell is wrong with the Twilight Aspect? Supreme messenger of the heavens and guardian of intense, world-shattering magical might, one day happens to notice this very same bratty little kid and say "Oh, I know. Let's invest in her all of my power and trust her with all of my mind-boggling and reality-warping duties. Even better, this last little test proves her total lack of respect for authority!". It gets worse. Zoe's whole place amongst the pantheon of Aspects seems muddled. She treats Aurelion Sol like a pet just because she can (due to his Targonian crown), tormenting him because she knows he can't really fight back. As an afterthought they throw in the fact that she occasionally fights Pantheon (What? Isn't she just a glorified Hermes? How does she beat Ares with regularity?), and in her color piece cutesily drop that there's a World Rune just sitting around. She has a huge crush on Ezreal and is spiteful and jealous towards Lux, which is odd, since her color piece makes it clear that she has the social intelligence of a 5 year old; she's been gone for millenia and doesn't have much grasp on her portal usage; when did she go to Demacia? Run into Ezreal? How does she know who either of them are? She treats her job like a joke and seems to spend more time tormenting squirrels than actually carrying out her duties, which, when you think about it, seem pretty fucking important. Why is she called the Aspect of Twilight, and how does that moniker relate at all to mischief or imagination? In what way is she linked to someone like Shen (The EYE of Twilight) or the Kinkou? Why is she still allowed to run unchecked and unsupervised with all this immense cosmic power when she doesn't use it responsibly? (Check out this post by Echoing, which highlights all the problems with Zoe's color piece in particular). By the end of her color piece, she's basically murdered an entire town using her magic without a second thought, all because they rightly freak out and send guards to drive her away when she uses magic to mess with some kids nearby. She isn't even 'tricky' or 'mischievous' like her ingame kit actually does a good job of portraying - she obliterates a town with a huge arcane meteor like a vengeful deity. She doesn't act like a curious teenager, more like a nosy little kid who completely lacks any form of common sense or social skills and acts with reckless abandon. Zoe's presence within the world of Runeterra is the contemporary analogue of an immature toddler's fingers on a thousand nuclear buttons.
I get Riot wanting to make a fun, outgoing, maybe even a little obnoxious character like Lux; we did in fact recently have a string of moody and/or dark champions like Kayn, Urgot, Eve, and Ornn. But there's a difference with creating a fun-loving bubble mage with a spoiled little kid who bullies those who can't fight back and treats her power like a joke. Take a character like Aang, from the critically acclaimed (and one of my favorites) TV show Avatar: The Last Airbender. Aang is a fun-loving air monk who is both mischievous and yeah, maybe a little lazy, a little too blase with his airbending powers at first. But over his narrative arc he learns the weight and gravity of his powers and responsibilities as the Avatar - he learns from his mistakes, understands how to rectify them, and begins to process the importance of things such as community, family, and the dignity of human life. Where he grows and learns from his mistakes in less than a year, Zoe revels in her own gleeful lack of work ethic, empathy, or humility for millenia. She's stuck as an obnoxious brat with immense power and no desire to change or learn - Aang embraces his gifts and uses them to protect and nurture, as well as fulfill his destiny to protect the people of his world. The parallels are rather striking.
TL;DR There are a lot of things wrong with Zoe thematically and narratively. She's a spoiled brat who disrespects authority and has used her power to hurt, bully, and even kill others without a second thought. She shirks her incredibly important responsibilities and the Twilight Aspect's decision to give her all this power makes zero sense. Her place within the Aspects is muddled and not clearly explained, and she seems more like an ill-contrived plot device to give Targon more firepower against the Void than a succinct and well-concieved champion in her own right. She's bratty and unintuitive, and her personality is not only obnoxious but clashes horribly with the immense power she wields. Riot has mistaken a lazy, bratty, and self-serving nuisance for the genuinely endearing innocence of youth. Its a wonder she hasn't already destroyed Runeterra, and I eagerly await more information on her because I'm really hoping this isn't the best Riot's stellar and consistently incredibly lore team can do nowadays.
