That said, I like your suggestions. There’s altogether too little introspection on what the point of schooling should be. To my mind, better that schools impart the metacognitive skills to be a better learner, a better thinker, a more stable person, than to impart specific knowledge.
Not my intention at all. I'm using the story as a jumping off point to reflect on our reality.
One sad, unloved wizarding student growing up to be an unstable adult is a personal tragedy. When that young adult decides that his problems are the existence of certain others and drums up supporters and starts killing people on a massive scale. That is a societal tragedy now.
Now obviously we don't have wizard lords in our existence. On the other hand we have unstable grown up former victims of Eton. And some might interpret the course of recent British political tragedies as an outward manifestation of their games. Providing a parallel to the story.
No poking holes at all.
This is why there was the german prejudice against the "perfid albion", because well the people who run that empire were deeply twisted and evil. The admiration for similar evil, ala hitler was only natural.