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.

It would also reflect terribly on Hermione. She'd be an utter fool to attempt that kind of thing without using Harry's brilliance and resourcefulness. Her influence over Harry is one of her most useful powers and killing stuff ingeniously (and surviving) is pretty much Harry's specialty. It isn't hers.

It's one thing to insist on having your own team in a school battle-games. It's quite another to waste the opportunity to accept aid (and in this case even leadership) from an ally in a situation that means the life and death of yourself and others. It'd be disgustingly immature, take 'silliness' to a whole new level and be completely irrational. Unless Hermione's goal in attacking Azkaban really is more about her ego and signalling and not about the need for Azkaban to be attacked for some direct reason... and she had some reason to be completely confident that it wouldn't kill her.

No respect points for ego when it is at the expense of shut up and multiply.