The story is sort of exploring the theme of how hierarchies reproduce themselves through abuse, coercion, and violence. Tsukasa isn't out killing monsters as part of some master plan—he's doing it in spite of one, because his grandfather threatened to kill Aju if he didn't. She's likely aware of that, and I don't think she's so altruistic as to submit to a death that is almost certainly guaranteed to traumatize Tsukasa into compliance. They accept this is how things just are, and hope to change it in the future.
However, Tsukasa being the designated monster slayer is essentially a hazing ritual to make him complicit in upholding the existing power structure. A person who commits atrocities will almost certainly never be able to regain the trust needed to negotiate a lasting peace, and so the family's position at the top of the hierarchy, not to mention their extremist position towards monsters, will be maintained for another generation.
You also catch bits and pieces of how those dynamics perpetuate the power structure, whether it's Urabe losing a loved one to violence (presumably by an ogre's hands) and the Watanabe group playing on her insecurities as a woman in a leadership position, to Hinata being coerced into her role as the next Shuten-doji despite her desire to escape that role.
That's what Naori and Hinata have to wrestle with if they want to be together. They are a same-sex, interracial couple in a violently conservative society, and their relationship carries a freightload of historical baggage that they have to deal with in some way or another. They can either confront the system or run away from it, but either choice carries its own set of problems.
That a good point. I guess my problem is the severity of the situation. I appreciate a character so grits their teeth and suffers through the bad times when it's their own mistreatment, but when you move up to murder I think it just goes that step to far to still make me empathize with them. Especially since Tsukasa is staring to look a little to far gone, hunting down the fox that was already beaten and ran away (though that could be my personal bias against tragedy to that level).
The part that especially bugs me is Naori's reaction. Sure Aju may not be that altruistic, she Naori is. So to have her hear that Tsukasa is a monster slayer and have response be, essentially, nothing honestly feels like the wrong response. For someone who has, on multiple occasions, defended monster who have tried to hurt or kill her, I would expect something stronger in opposition to innocents being killed. Like a "I don't think I can trust you anymore" or something.
I just fear that this is going to end very anti-climatically and just sweep the mass-murdering thing under the rug. I'm afraid these atrocities are just gonna be blamed on the older generation and our "tragic heroes" are just gonna get to wash there hands of the whole affair. Sincerely hope I'm wrong though.