I don't think I would assert that intelligence, science or rationality is the Ultimate Power on the individual level. But your argument to that point doesn't work at all, afaict.

We know, as a matter of historical fact, that Adolf Hitler and his Nazi Party, despite being generally incompetent, unintelligent, irrational, superstitious and just plain insane, managed to take over a country of tens of millions of people from nothing, in the span of fifteen years.

What evidence is there that they were generally incompetent, unintelligent or irrational? They certainly were in some instances (efforts at racial categorization were certainly a waste of resources) but the instances of irrationality can almost always be traced to events that harmed Nazi Germany in some way. Hitler's poor military decisions were what brought them down. On the other hand, investment in the sciences gave them distinct advantages over their enemies. Certainly their ideology involved holding false beliefs that undermined their science (expelling Jewish physicists was definitely harmful) but a good deal of their science was just fine. Is there any indication that the German state was run less efficiently than the other major powers?