it's quite clear that everything is deliberately vague beyond the borders of the US
It's her ignorance of the USA, especially functioning capitalism and a functioning state with elected officials where she has such breathtaking ignorance. Atlas Shrugged could be renamed "Bring back the Tsar and his petty nobles to run the place", so much of it is about the horror of dirty little serfs like the science guy having positions of power.
And seriously, how is Rand supposed to have undermined democracy anyway?
Her aristocratic manifesto was taken seriously be far too many people who take it far more seriously than a shallow SF book should be.
I note that we in the US currently have a president who is the antithesis of anything Rand believed in,
If you pay attention you'll notice that they have ALL been that from George Washington onwards. IMHO that shows more about Rand's lack of understanding of the USA in the years when she wrote the novel than anything wrong with the United States.
It's a European novel about aristocracy (screwing their way to the top as jailbait no less), highly critical about egalitarian colonials like the people who built the United States and those who carry on inspired by them. It's had a LOT of influence on people who didn't know better and it's distorted their view of reality.
If you want to read something to defuse such shit try some Joseph Conrad - well written, lots of it is short, and he made sure he had a very deep understanding of the topics he wrote about. "Under Western Eyes" shows what Rand had to be afraid of in her earlier years and it's a pity she never wrote something like that instead of her big insult to the west "Atlas Shrugged".