You're speculating that a US president has a relatively average intelligence - why are you assuming that? The top job in a democracy is generally one of the most competitive positions in the world and US presidents are typically exceptional in multiple different ways. It'd be really surprising to have a US president with an IQ below something like 120 and I'd personally be assuming >140 for the average. As far as I can see a 140 IQ is around the 0.1-1% mark, it isn't that rare compared to presidents (<0.01%).
> 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.