I agree with the letter "The Appointed Judges" that we are not a pure democracy. But this is not because we are a union of states.
We should remember that "states' rights" was the main rationale of slavery and the seed of the Civil War. Because of that, the nation added to the Constitution a limit to "states' rights" to prevent an abuse of the people, in particular, the 14th Amendment.
We live in a nation; we are bound by the agreement made at the time that union was joined and to which every subsequent state accepted. Each of the 50 states is part of that pact.