For instance, until the discovery of nuclear weapons, armed conflict was often a primary means of settling disputes between nation-states. However, if you tried to settle your dispute with your neighbor, or your company's dispute with its competitor, using armed force, it would achieve nothing except getting you thrown in prison.

This is really, really false. People use armed force all the time with their neighbors. Just like at the national level, armed force is very effective as long as no one bigger and badder will smack you down for using it, as they almost always will if you're a corporation operating on a large scale in an industrialized nation. The situation is virtually identical.

On a separate point, while the Nazis had some crazy beliefs, they still excelled in a number of important areas. A superintelligence trying to figure out how to take over a country would probably create a public enemy and invoke as much Nationalism as possible, and publish lots of propaganda, and indoctrinate the youth, and establish a cult of the leader, and so forth. Acting rationally does not mean winning your opponent over with well-reasoned blog posts, unless those are the most effective means you have of getting to him. Acting rationally means using the means that will accomplish your desired ends most effectively.

If the Nazis had had their crazy values but actually been rational and carried out their war differently (less aggression towards Russia, not dragging the US in, delaying the Holocaust until they could actually afford the military resources for it), they could have been a whole lot more successful than they actually were. So let's be glad they underrated rationality.