I'm just an amateur occasional Supreme Court-watcher, but just reading his dissent I wouldn't go so far as to say he thinks schools need to be more constrained

I'm just an amateur occasional Supreme Court-watcher, but just reading his dissent I wouldn't go so far as to say he thinks schools need to be more constrained than the majority does. He might or he might not. Or maybe I missed something you picked up on. What is clear to me is that he thinks there are crucial unresolved issues that the majority punted on. The process of the court's opinion-writing sometimes involves several justices circulating draft opinions and trying to recruit others to sign on. Thomas might have written such a draft opinion with very careful reasoning, perhaps even concurring in the majority's judgment, but nobody else was willing to sign on to some of his specific reasoning that he thought was crucial, so he took his toys and went home.