Hence, the Nazis, who were really irrational, succeeded at taking over Germany, but then failed at taking over the world largely through irrational stupidity.

Certainly, sufficiently great (superhuman) rationality and intelligence could have taken over the world. But I'm not convinced that a group of sane, rational, intelligent mere humans at the head of Nazi Germany had a high probability of conquering the whole world (which would include the USA). The Nazis already did much better than could be expected on average for humans. How much better than that could you be, if you were in their place? What would you do exactly?