When I think about questions like these, I recall the Anthropic Principle. Perhaps on lots of planets, intelligent life ceased at the beginning of the Atomic Age. Here we are seven decades (several generations!) in, and we're still alive! The numerator on the odds almost doesn't matter, when you never get to see the denominator. Now that we're finding all these planets, perhaps we ought to start looking for nuclear extinction events? They probably wouldn't leave lasting evidence, but if they're common enough they wouldn't need to...

Actually the accounts I've read seem to indicate that most missile operators simply decided they would never launch no matter what. God bless them, for that.