As has been explained in more detail by more capable media critics than me, Harry Potter's overall narrative arc is about restoring bureaucracy, not overthrowing it. The problem are never the systems but individuals abusing them because they're evil (with little motivation given).

If anything, framing it as "the bureaucracy overthrowing the hero" (or the hero making peace with the system, for a less dramatic interpretation) is only wrong because this implies the hero was ever at odds with the system to begin with. The system is never questioned (except by Hermione, who is portrayed as annoying an naive when she does it), only individual bad actors are identified defeated.

The ending of Harry Potter does not have wizards living openly alongside muggles, house elves liberated, mutual respect and trust between wizards and goblins, or the abolition of the Ministry. Instead it shows the next generation of students getting to experience the same exciting start in their train ride to Hogwarts with the implication that this time, things will be different because the evil people are REALLY gone this time.

Harry Potter is distinctly about protecting the "sanctity" of institutions, at the expense of individuality. Umbridge may be the personification of bureaucracy in our minds, but in JKR's, she's a threat to the image of British boarding schools being elite, character-building places for children. Note that, as a disciplinarian, she's functionally equivalent to Snape. That was not Umbridge's "sin". Her sin was teaching to the test, removing the academic rigor of Hogwarts, presumably leaving it on par with lesser schools.

We might even look at her clothing and, in our minds, it looks very conservative. But in the wizard world, we never see anyone wearing such outlandishly colorful clothing. What looks like a makeup MLM saleswoman's outfit to us is a radical expression of individual style in the HP world.

In Harry Potter, individuality comes at a price. The more you express individualistic thought, living outside of the norms of society, the more impoverished you need to be to remain "good". Look at the Weasleys. Look at the Lovegoods. Those that attempt to be successful and individuals are default evil.

HP is so incredibly conservative, it's surprising everyone was surprised by JKR's politics.

Harry's single ambition through the books is becoming a member of the Wizarding police/SWAT team (Aurors), totally integrated into the system. The only things he had any personal problem with was occasionally who's in charge. In fact, he stays (almost) moot through the entire series of books on questions such as the fact of elves being literal slaves, where people who speak out (e.g. Hermione) are portrayed as shrill whiners.