Yeah, we haven't missed the point. Strangelove occurred to me but if you remember the movie, AI wasn't involved. The Soviets had simply put in a simple rule that if war started, their system would irrevocably respond with all nukes.

There has been some pretty intelligent sci-fi written about AI and other subjects which humankind is still far from catching up with. I remember a sci-fi book of psychological stories which included a tale in which a member of a large cloned worker group had to deal with loneliness after an accident took his siblings away.

One of the sci-fi tropes that continually bugs me is to be found in many many movies with robots used as soldiers. If this ever happened, you'd find that the robots don't miss when they fire at you.