Yall forgetting that Liz has already been confirmed to be the Saint, which comes with unprecedented magical power. So far, the most in depth magic we know about is Alicia's dark magic, so for all we know, Liz might actually be unwittingly casting magic that is similar to charm. If we add that onto her clearly already strong natural charisma, it's easy to see why a majority of the student body are basically sheep; real life cult leaders are often incredibly charismatic people with strong convictions which is exactly what's happened with Liz here whether she realizes it or not. It's why Alicia is picked out specifically to monitor her: the adults can see that she's functionally created an echo chamber for herself because her immensely charmed life full of people who turn into her yes-men has led her to be intensely idealistic, being ironically bigoted in her belief that equality and everlasting world peace can be achieved simply by holding hands and thinking happy thoughts. Alicia is meant to act as her voice of reason, to break through with a dose of practical reality and force her out of that narrow view of a perfect world so that when Liz does take up the mantle of Saint, she doesn't accidently send the kingdom's future straight to destruction and collapse on a road paved with good intentions.
It's not that Liz herself is a bad person. As far as we've been shown, she genuinely wants to make things better, to change the world so that it will be a place filled with love and light where everyone is treated with dignity and fairness. But as we've seen with her behaviour over and over, she's been so bubble wrapped by the goodness and peace she's experienced in her own life that she cannot comprehend a world that lacks it, even when it's right in front of her. It's why she almost gets Alicia killed; in her eyes, at that moment, she stops Alicia from hurting another human because it's the imminent threat, but she doesn't also paralyze the man because the thought of the possibility of him using that moment to harm Alicia doesn't even exist in her head. Even fully seeing that Alicia is a wreck and injured, she doesn't register that the men are responsible since it didn't happen right in front of her, because Liz herself wouldn't do it, and she assumed everyone would think like she would, because she grew up in an environment that always agreed with her. It's why she can keep preaching that violence is never the answer, it's why so many of her thesis papers are so immensely flawed: because she's clearly never had to experience a situation where she HAD to defend herself using force (someone will always show up at the slightest hint of a threat to protect her from it), because she's never had to experience the repercussions of her thoughtlessly idealistic methodologies affecting others.
The little extra, at least, shows that she's... maybe taking Alicia's critiques and proofreading seriously? That she's finally getting some character development through that naive cotton candy flower field in her head and realizing things aren't as charmed as she thinks they are? Hopefully? Cuz as the royal council did say before, Liz is capable of enacting incredible positive change and prosperity for the kingdom, but only if she's able to wisely and pragmatically plan out her vision with full understanding of the harsh realities of the world.
That said, if she takes the rival thing the wrong way and decides to go after Duke romantically, she can eat sewer sludge. That boy be Alicia's, fuck all the way off.