Constitution Article VI, paragraph 2 states
This Constitution, and the Laws of the United States which shall be made in Pursuance thereof; and all Treaties made, or which shall be made, under the Authority of the United States, shall be the supreme Law of the Land; and the Judges in every State shall be bound thereby, any Thing in the Constitution or Laws of any State to the Contrary notwithstanding.
Now, I just finished reading the entire Constitution again; and, I still didn't see anything at all that would lead me to believe that schools cannot be created by the either the state or federal government. If you think such is the case, please quote it so that we can discuss it. I am ready, willing, and able to discuss this objectively. Are you?
On the other hand, I can exhibit: Jefferson's Bill https://founders.archives.gov/documents/Jefferson/03-12-02-0095. This bill was for his state, but it didn't pass. Another form passed later.
No thanks. I think you argue in bad faith.