In practice, Americans supported their own independence, and they support independence for eg. Taiwan, but they don't support independence for the Confederacy because that would entail weakening their own nation. To the extent that anyone will try to rationalise the American Civil War, they might reach for slavery, but a philosophical belief that political union is absolute and nobody can declare independence is not it; at most that's just a flimsy post-facto justification for the already-decided fact that states must not allowed to secede for power reasons, and this is evident from the fact they don't condemn their own revolution and advocate for return to British governance.
Very self-serving that you believe superintelligent AI is going to tell people your ideas are the best ones, incidentally.