But Hermione isn't really rational, she's just intelligent. I don't think she can perform a feat of astounding rationality in this fic, as you are suggesting. Her idea of morality is flawed and naive. If I imagine her going to Azkaban and destroying it, it would be for decidedly uninspiring reasons to me, as a rationalist.
No offense (and I'm a boy so quite probably biased about this, fair warning) but are you sure you know what girls are like in real life? I know in a utopian world there would be no gender stereotyping, but in my honest experience, even as someone who strongly wishes stereotypes would all burn and die, girls in schools do gossip, and stress about relationships, and quite possibly are prone to sensitivity and preoccupation about love, even if it is culturally rooted.
Just wondering I guess if you've been so successful in emancipating yourself from that stereo...
Up until I was about Hermione's age, my friends were nearly all girls, and they were an even mix beyond that. I am not claiming anything so preposterous as that girls do not gossip or fixate on interpersonal matters. Of course they do; it's not even limited to children. I am saying that girls are not uniformly silly creatures, differentiated only by name, approximate g factor, and school House.
Penalty for incorrect use of the word 'literal'.