Sigrid Ellis makes a great point here: the economies of most post-apocolyptic stories are ridiculous. (As she says) We know from viking records how many warriors an agrarian society can support. “Your town has 500 people? Then you get five full-time non-food-producers, maybe. That’s warriors, mayors, librarians, etc.” Nobody gets a giant army.
Lots of people have agreed but realised they had no idea how pre-industrialised economies work. Ellis has helpfully provided a list of good places to start.