> von Neumann's fear was that nuclear war was inevitable

Ethics is messy, but in this case he made an actual, verifiable prediction: that the USSR would use their nuclear arsenal and unleash nuclear war. He said "With the Russians it is not a question of whether but of when." Not that we would come close to nuclear war, or that it would have a high probability that it would happen. He stated that it definitely would happen. And he stated this very confidently.

This prediction turned out to be false: the USSR collapsed before it used its nuclear arsenal aggressively, and modern Russia still has not used its nuclear arsenal in any other capacity than as a vague threat.

We can state unequivocally that he was wrong about this. Reality disproved his game-theoretic argument.