I mean, even though people are saying "Why doesn't Charon just kill Haumea?", I don't think he can. Yona and the other demons and psychos in charge of the White-Clad aren't going to let him: she's their most valuable asset since she has a direct line to the Evangelist. Plus, if it's part of Charon's religious beliefs that "Haumea was given this power by god, whose will we should follow" then he wouldn't want to just off one girl. Haumea has had to listen to all of mankind's unconscious, evil thoughts from the time she was born, and Charon sees this child suffering because all of mankind is suffering and secretly wants to die. Causing the Cataclysm will 1. fulfill the Evangelist's will, 2. put mankind out of its suffering, just like it wants according to the collective unconscious, and 3. kill his otherwise unkillable little girl. If Charon isn't watching out for Haumea, who knows if someone else would work as hard to put her out of her misery? They might just let Yona and the others keep torturing her for who knows how long. Charon is going to end this.
I mean, I've been suicidal. What finally got me out of it was getting electroconvulsive therapy, i.e. they used electricity on my brain to cause seizures. It had some side effects like mood swings to the point my personality would be different (flat affect one day, manic the next), and memory loss. Now Haumea's brain is probably constantly irritated by electricity, so that's already going to make her hella unpredictable and pissy, THEN she has to constantly hear how mankind wants to destroy itself? THEN she's basically imprisoned and tortured by a literal demon for her whole life who's convinced her that burning the world is the best solution? Of course she's going to go along with it: she's been driven insane. Then you get her only friend—or at least the only guy who cares about her—to watch a little kid's mind be destroyed by evil superpowers. Of course he's going to go along with it too. Charon and Haumea aren't like Arrow and Sho: they can't get away. Sho can stop time and stab people, big deal. Who cares if he's there or not? When he escapes, they don't even bother to look for him.
Electroconvulsive therapy probably saved my life, and I'm still on four medications.