“and those principles won’t even prevail in the smaller successor state”
But they don’t prevail now, so what do we lose? World prestige? Military power? Oh, no!/s
Sure. But more to the point, we'll come to be seen as a failed state that couldn't even hold itself together.
Some rump state isn't even going to be very convincing in what it believes or in its ability to pass on what the secessionists claim to believe to the next generation.
Give up Washington, DC, Gettysburg, Independence Hall, Plymouth Rock, probably Mt. Rushmore and Mt. Vernon, and what do you have left?
Of course secessionists are going to deny that, but the bravado covers a lot of insecurity about whether secession would really bring about the effects you think it would.