While the nuclear capabilities may not deter the beginning of the war but if the political will is there to use that capability after such an attack, then it would possibly be a short war. So Red decides to strike and Blue returns with a nuke or three or dozen, exercise over. What's the point in that?

But you are right, history shows that a "deterrent" of any nature, not just related to war, is often not considered leading up to whatever it is supposed to deter.