I hadn't really thought about the story being a cold war era one until you mentioned it (I didn't actually know how old the book was, admittedly), but it actually does make a lot of sense out of the way in which it's structured -- the "two superpowers want to destroy the world to see who will win between the televangelist and the failed revolutionaries" is a VERY US vs USSR framing. Of course, Christian fundamentalism as a driver of US politics and its relationship to domestic misery and imperial expansion is, you know, alive and well (Mike fucking Pence is the fucking VP) but as you indicate there's something a little out of step in the world that this depicts. I think the Four Horsemen could indeed have been used better, as you say, on this point.
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(Anyway, criticisms aside, I liked it!)