This seems like an exercise in scaling laws.
The odds of being a hero who save 100 lives are less 1% of the odds of being a hero who saves 1 life. So in the absence of good data about being a hero who saves 10^100 lives, we should assume that the odds are much, much less than 1/(10^100).
In other words, for certain claims, the size of the claim itself lowers the probability.
More pedestrian example: ISTR your odds of becoming a musician earning over $1 million a year are much, much less than 1% of your odds of becoming a musician who earns over $10,000 a year.
The boys get the HPMOR equivalent of "I want to be a selfless doctor" or "I want to be an important politician."
The girls get the equivalent of "I don't want to be like my relatives" or "I want to be adored by lots of men".
The girls' aims seem defined by types of relationships, which makes them more fragile and harder to visualize than aiming for a type of occupation.
This doesn't mean that Padma wouldn't be cool in reality. (Real-life outcomes seem determined as much by search method as by deliberately planned destinations.) But in a story, it gives her less narrative impact.
A Hermione who risks all against Dementors "to help Harry" is not nearly as interesting to me as a Hermione who risks all against Dementors because they're evil regardless of Harry.
We'll all help our friends. Pick any evil person in history -- they had friends. If they're a political leader, they had lots of admirers.
The fic itself has Harry make the point that if you're only interesting in helping an "us" and not a "them", that's a pretty weak sort of good that easily turns to evil.
I think in a fic so full of extraordinary characters, Hermione deserves to be extraordinary enough to do awesome things even for strangers, even when she doesn't think her friends will benefit, because a world without dementors is just better.
I am confused. What would you suggest as an example of an "inspiring reason" to go and destroy Azkaban, that does occur or could occur to Harry, that would not normally occur to Hermione?
Oh, good point, the author's prepared for Hermione to take on Azkaban. The trick will be motive.
If Hermione harrows Azkaban for Harry's sake, that's Hermione the faithful NPC, not Hermione who has wishes and dreams of her own.
If Hermione harrows Azkaban because it's the right thing to do, that will be pure awesome.
As you say, if Hermione believes Harry is dead, especially if she believes some other innocent is about to be sent to Azkaban, she could spring into action quite on her own.
I think you've convinced me 66% that Hermione, not Harry, takes on Azkaban.
What I don't feel so confident of is that the author will manage to do this in a way that Hermione's motive is "because it's the right thing". The gravitational pull of "Harry causes all interesting good things" is strong.
Avoiding the "Harry causes everything good" gravitational field isn't an insoluble problem. But EY has a lot of other balls to juggle besides the harrowing of Azkaban.
Yes, to make it plausible you do have to put Hermione in an impatient or infuriated state of mind, and Harry has to be out of contact. So, for example, suppose:
Harry is elsewhere, preparing his next move against Voldemort; and
Hermione gets dragged to Azkaban on a visit by someone intending to intimidate her, and she concludes it is just as monstrous as Harry thinks. (Actually, she'd probably be even less tolerant: Hermione is not a lesser-evil-excusing sort of person, once you jolt her out of her status-quo bias.)
You could argue that would be enough -- Hermione is good at hard work and righteous indignation, and she and Harry could be arranged by the author to have discussed hypothetical Azkaban strategies beforehand. If you wanted added pressure on Hermione,
In which case Hermione might rationally decide to "go out with a bang."
The hardest part of this (in a literary sense) would be keeping Harry away from Hermione for the critical period.
You're right, there's nothing absurd, individually, about the mostly-male lead adults, the author's distaste for sports comedy, and having Hermione and McGonagall be far less hubristic than the men.
The author is largely following canon in each of these, except for minimizing Quidditch (for which I, for one, am heartily grateful) and for adding in shipping humor (which I also like). The trouble is the cumulative effect.
I see not the slightest evidence that the author wants Hermione and the other females to come off as narratively second-best to the men.
But in the absence of a positive force impelling Hermione et al toward narrative grandeur, they end up being defined as compliant like McGonagall, or trivial like the romantic gossipers, NPCs rather than PCs in either case.
EY observes that Hermione doesn't need more brainpower to be a force in the story. Unfortunately, since she's in a story, not a collection of biographies, she does need more narrative impetus to get her to engage in story-like behavior alongside the men.
The same is true, at a smaller scale, for Padma as versus Neville and Blaise. The boys have tolerably specific ambitions; the girls don't. Hermione wants to be "a hero"; Harry has a list of specific large problems he's aiming to solve. The narrative outcome was inevitable.
When your main characters are as aggressive and grandiose as Harry and Quirrellmort, anybody without an active force to make them narratively prominent ends up looking second-rate.
Ooh, Hermione versus Azkaban. I want that.
If Hermione takes down Azkaban and survives, and does so without Harry seeming to take control, that would be more amazing to read than I can possibly express.
Also it would be a nice touch of realism: no one good person solves all the problems.
But there are three hard literary problems here:
the author has probably got another Azkaban answer in mind, based on Harry,
the author would have to prepare the ground for Hermione grokking the "Death ain't inevitable" approach to Dementors,
it would be tricky to write a realistic Harry who, even from Harry and the reader's POV, was "protecting Hermione's back while she saves the day" as opposed to "rescuing Hermione". The rearguard samurai who buys the hero time is a fiction staple, but it's not a default role for Harry.
[Edit: ] as wedrifid wisely points out below, Hermione has to have a good reason to believe she has to take the lead, since Harry is demonstrably better at the average Confrontational Solution than she is.
But if it happens I will be ever so happy.
Yes, that's it: the girls don't aim for distinctive future selves, the boys do.
Blaise and Neville are each trying to become something, and it's something different in each case. The girls? Not nearly so much.
Prediction 1: Hermione will soon harrow Azkaban. Why wouldn't she? She's all but immortal, now.
Prediction 2: Time-travel and memory-charm shenanigans incoming. Evidence:
Harry weirdly ignored the missing recognition code on LV's forged message.
Cedric considered in Harry's plans, and his Time-Turner mentioned, then seemingly forgotten.
Death-Eaters all dead, but no faces observed.
Flamel asserted dead, but we didn't see it, and LV explicitly didn't kill him personally.
Dumbledore thinks in stories, yet we're supposed to believe he's surprised when the villain reveals he's captured the hero and his equipment (Harry and the Cloak), just like villains always catch heroes and take their stuff near the end (see: Frodo Baggins, Luke Skywalker).
Hermione has been asleep the whole time, neither giving nor receiving information.
Questions:
did Harry tell Cedric to do certain things before Harry left? Did Harry tell Cedric to Obliviate Harry afterward so Harry could play his part convincingly? What did Harry most likely tell Cedric to do?
who will do the Time-Turning, Hermione, Cedric, or Harry?
who will be saved? Obvious candidates include Flamel, Dumbledore, Lucius Malfoy, maybe all the anonymous Death-Eaters.
if you were Hermione and had a Time-Turner and the Stone and the Cloak and six hours to save everybody but Voldemort, Quirrell and Macnair, how would you do it? (Do you need the help of someone who can Obliviate well? Do you need partial Transfiguration?)