Yeah I think Miller was using the nuclear holocaust as a vehicle to reflect on original sin (i.e., the inevitable tendency of human beings to engage in self-destructive behavior) and the antidote to it offered by the Catholic Church. If he had written the novel today it probably would have been something other than MAD that nearly wiped out civilization twice.
(A) I don't see it as a failed prediction, that's the author's view. Me, I think history is a long time compared to the time we've lived with WMD.
(B) The type of literature in question is called an allegory. To see an allegory as a prediction is... aligned with why people write them. I wouldn't call picking the wrong definition to support an argument simpleminded; perhaps friction-seeking would be a good term.