> You're speculating that a US president has a relatively average intelligence - why are you assuming that
I am not assuming that: any range that has studying nuclear engineering as its floor is above average intelligence. I thought it was self-evident, but apparently not - perhaps not many people know what a "Navy Nuke officer" is. To be more explicit the range is between above average intelligence and "genius". Regardless, I will never be convinced that people with relatively average intelligence are precluded from greatness; so excuse my scepticism when fellow nerds pat themselves on the back for being the engine of the world without pointing at any research that bears this idea out.
> To be more explicit the range is between above average intelligence and "genius".
You haven't made your point explicit. So what? What are you basing your argument on here? The existence of Navy Nuke officers may well have no bearing at all on Carter's intelligence. If Mr Carter was trying for jobs which required genius that suggests he was one.
> I will never be convinced that people with relatively average intelligence are precluded from greatness
Greatness is one thing, competition for US presidency is something else. I'm sure it is possible and happens on rare occasions, but an ordinary person cannot be reasonably expected make it through the scrum to become a US president. They usually have to have quite a few somethings to set them apart from the crowd - including great intelligence.