Criticism that’s primarily transmitted by teachers is limited in scope; after all, most people who have read this series have not done it because of its place on some curriculum (and, at least in the US, where various politically powerful groups see it as problematic for very different reasons, children often read it in spite of educational institutions).
The most sensible mechanism for transmitting criticism is probably another work of fiction — one that makes the implicit problems in the Harry Potter universe more explicit. Such fiction is relatively rare (the closest I’m aware of is Lev Grossman’s The Magicians and Elizer Yudkowsky’s Harry Potter and the Methods of Rationality, and of the two, The Magicians comes closer to a real criticism of the pedagogy despite making the focus a significantly more progressive institution and barely touching upon the arbitrary segmentation).
There are lots of low-hanging fruit here. Consider a Harry Potter like story where the Dumbledore character is the antagonist — an initially charismatic and likeable character who is later revealed to be using his institutional power to extend a vendetta against the Voldemort stand-in who was a scapegoat for Dumbledore’s actions taken as part of his rise to power. Or, consider the possibilities of expanding the focus on the Hagrid character — someone who becomes a tool of an institution because the difference between his gentle nature and his imposing physical presence makes him shunned by most of society and therefore easily manipulated by anybody who shows him kindness. Where The Magicians focuses on breaking down the idea of the institution as necessarily mostly-good (by amplifying the kind of dangers already present in Harry Potter’s institution) and breaking down the idea of the chosen one (by making the protagonist an outsider whose drive causes him to keep showing up even though he almost inevitably fails), and HPMOR mostly focuses on breaking down traditionalism, serious criticism of class and institutional power in Harry Potter is rare.
If we had a proliferation of stories that deconstruct the assumptions of Harry Potter, people would naturally come to occasionally read them in conjunction with each other; furthermore, teachers could assign them together (in the same way that teachers often assign students to read both 1984 and Brave New World).
The Harry Potter universe is a master-class in dysfunctional power structures that almost every reader managed to sleep through. Exposing it through narrative means has enormous value.