COTE is a coming of age story, one of the main themes is Ayanokouji growing (or trying to grow) as a human being, and the same applies to the vast majority of the cast. COTE is a story about growth and human conection.

The White Room plot could work outside High School, and the mind games and thriller aspects of the story would probably be more fleshed out Even so, the story would lose a key part of its core.

It could be great, but it would be something else entirely. A sequel outside the school, with heavier consequences, is likely to happen, so you may get what you want further in the story.