Merneith is at the same time cute and a complete psycho, but in a different way than the raider sisters.
She's in her own way more level headed and of course also much more powerful.
Actually Merneith seems to be a more competent ruler then we are inclined to think.
When we see a work of fiction we tend inconsciously place charactes in classic roles box, and the box for Merneith is either that of the evil tyrant of the mad king because she has been introduced as arrogant (how she tries to treat Zaton after the first mission) and crazy and sadistic (the execution scene). Yet later she shows to understand rather well the nuisances of politics and public image. She seems to have quite a grasp of the art of government and she can have a commanding presence.
So, i think her main 'problem' is supposed to be young, insecure, immagure and lacking experience, while she still has talent for her role.
When she tries to dominate Zaton or when she play in a sadistic way at the execution she literally behave like a child. She even needs to show up to a pier of hers (Zaton's daughter). When she takes decisions she's overall competent and misured but she also can be brash and in need of advice.
I think her actual role is that of a 'monarc to be'. A youngster who need help to become the talent she's mean to be. For example like Emperor Meiji in the Last Samurai, who is portraied like a shy and curious young man controlled by his ministers until he finds his wisdom thanks to Katsumoto or King Arthur in Disney's the Sword in the Stone, who literally follow his mentor figure Merlin who teaches him the foresight he will need to rule.
That's why i think her narrative arc is going to be about Zaton helping her to mature, find her resolution and refine her natural talents to become a wise queen. Among Zaton's character traits , he is a father and while he is a daughters banging father, but this is normal in Zeta, he seems to be a good one who rised well two smart and strong daugher. Merneith could kinda be the third.