It’s a distinction without a difference. Schools aren’t on the list, then they aren’t on the list. Article I, Section 8 is not very long.
The Bill of Rights is irrelevant here, it’s the rest of the Constitution that’s at issue. Schools are something that belongs not even to the states, but to the people and families. There’s no need for government of any kind in this business. There’s no benefit to welcoming poisonous government into the mix, you have done this purely voluntary.
There is no list of what they are allowed to do. There is only a list of what they cannot do. If you think otherwise, please post appropriate reference material that supports your view. Otherwise, you are just voicing an opinion; and, opinions are not actionable.