The Romans, I'm guessing, probably thought that all of history up to that point had led to their ascension. It's likely that they could not see past their own dominance of the known world at the time to comprehend the idea that their empire had an inevitable shelf life. Like the jellyfish in Quinn's tale, the average Roman citizen couldn't see past the "lip of the vast bowl that holds the sea."
I'd hazard a guess that the Aztecs were no precognitive than the Romans. Neither were the Greeks. The Han Dynasty? Nope.