Pseudo-scientists were doing that before the bombs fell. FEV, some of the nastier creatures like Deathclaws, the origins of Ghouls, and the guy who became The Master in FO 1 was all before the bombs.
Only two groups I can see actually recreating the USA as it was meant to be - The Enclave and Legion. . .ok, I kid, seriously The Minutemen and Disciple of the Apocalypse('cause they want to use technology to help, not hoard it like the Brotherhood of Steel). An interesting thing about the Minutemen is that the first version were basically cops. In the new version that's created when siding with them is more along the lines of what the Founders kind of intended - that people didn't have to wait for a sheriff or whoever to save them. That people can properly defend themselves without paying some kind of price for doing it.
The barter system is a type of capitalism in itself. Heck, I do more trading with ammo that I'll never use instead of the actual game currency. . .so not only do I trade in lead during a fight but also when buying stuff.
Another difference between a capitalist and a communist is that a capitalist knows the system isn't perfect and acknowledges a lot of things can and will go sideways if not careful. A communist on the other hand will say their system is perfect. And that's why whenever communism fails or does something really evil a communist will say, "That wasn't true communism!"
The problem with China launching the bombs after winning a major victory doesn't make sense to me. Also why launch the bombs knowing the losing side would instantly launch theirs.