I mean, the "crew" constantly breaks school rules,

They violate curfew. Never once do they make any sort of stand against rules that are unjust.

fights injustice agains the school's evil teachers

Hagrid walks merrily into Azkaban. The closest they get to rebellion is hiding Sirius Black after he escapes - nobody ever lifts a finger to argue that maybe he's been wrongly accused.

undercuts the ministry.

The fuckin' minister shows up for Christmas. When he legit subverts the Weasley's son, they're all well shit I guess we lost a son.

They constantly point out how corrupt and mismanaged it is

And do exactly fuckall about it.

do what they need to do despite it being "illegal" or whatever.

"What they need to do" is invariably whatever Dumbledore tells them to.

Here's a story about a bunch of Norwegian schoolchildren who steal $9m worth of gold from the Nazis. It's not only old, it happens to be true. After five books (and the downfall of the liberal order), Harry and his friends get off their asses to infiltrate the MInistry of Magic but only after they spend half a book wandering aimlessly bemoaning their plight.

I guess as a kid reading it, it is more relatable.

This is my beef - as a kid, it is more relatable if you presume that kids should never question authority.

Because the world feels like a terrible place with shitty rules and plenty of "wrong" things going on, run by adults that don't really do anything about it.

You are exactly illustrating my problem - to you, the world is a terrible place and adults don't fix it. But the idea that as a kid, you have some agency over the terrible aspects of your life? That's completely alien to you.