Nothing un-PC in there that I can see! You uh, pretty much called it!
But think about it this way: if there were really strong cultural and linguistic differences (much bigger than OTL) plenty of people around the world would assume independence as the right of that region’s inhabitants, just as they would for, say, Afghanistan or Bhutan. Maybe creating stable, economically-diverse polities should be more of a requirement for nationhood, but the “modern” nation-state was built around the idea of self-determination more than viability.
We have many modern examples of nations that are basically propped up by larger, more prosperous nations.
To your claim that independence would make things worse, I’m certainly not going to disagree.
If I was going to correct any5ing in your statement, I might find a little issue with the characterization of Appalachians as rugged individualists. In the US that tends to conjur a pretty specific image. For me, at least, I think of ranchers in feuds with the Dept of the Interior, or people in Montana living off the grid.
Appalachians are certainly closer to that than some richer areas, but there’s a really strong communitarian strain as well. Lots of love, frozen in amber, for the New Deal and the TVA. And just a lot of bitterness (like enough that it dominates most political actions) about the times when things were better. A lot of this is the same myth of the rosy past sold to and by most conservatives, but in the case of Appalachia it really was demonstrably more prosperous in the past.