There's a correlation between IQ and leadership skills, but it's non-linear

I wish this article was several times longer than it actually is.

Although previous research has shown that groups with smarter leaders perform better by objective measures, some studies have hinted that followers might subjectively view leaders with stratospheric intellect as less effective. Decades ago Dean Simonton, a psychologist the University of California, Davis, proposed that brilliant leaders’ words may simply go over people’s heads, their solutions could be more complicated to implement and followers might find it harder to relate to them.

Well if you're not communicating in a way people can understand, you're not actually that bright. But more on that in a bit.

IQ positively correlated with ratings of leader effectiveness, strategy formation, vision and several other characteristics—up to a point. The ratings peaked at an IQ of around 120, which is higher than roughly 80 percent of office workers. Beyond that, the ratings declined. The researchers suggest the “ideal” IQ could be higher or lower in various fields, depending on whether technical versus social skills are more valued in a given work culture.

The study’s lead author, John Antonakis, a psychologist at the University of Lausanne in Switzerland, suggests leaders should use their intelligence to generate creative metaphors that will persuade and inspire others—the way former U.S. President Barack Obama did. “I think the only way a smart person can signal their intelligence appropriately and still connect with the people,” Antonakis says, “is to speak in charismatic ways.”

From The Idiot Brain :

I'm a neuroscientist by training, but I don't tell people this unless directly asked, because I once got the response, "Oh, think you're clever, do you ?" Do other people get this ? If you tell people you're an Olympic sprinter, does anyone ever say, "Oh, think you're fast, do you ?" This seems unlikely... Someone who is more intelligent than you presents an unknowable quantity, and as such they could behave in ways you can't predict or understand. This means the brain cannot work out whether they present a danger or not, and in this situation the old, "better safe than sorry" instinct is activated, triggering suspicion and hostility.

Which could suggest that people who are a little bit cleverer than average get away with it because they're viewed as basically normal but with an extra skill. Those who are quite a lot cleverer may be unpredictable and therefore viewed as dangerous to ordinary folk. How can you know what someone else is likely to do if they're thinking five steps ahead of you ? How can you trust they have your best intentions at heart ?

On the other hand, perhaps IQ is a better measure of analytical intelligence than emotional intelligence and/or empathy. Hence the sample may have really chosen people with strong analytic skills but less concern for their team members, making them genuinely ineffective leaders despite (say) mathematical brilliance. Though it's a vastly overblown stereotype, there certainly do exist people with genius skills in one narrow area who are lousy at almost everything else.

https://www.scientificamerican.com/article/why-people-dislike-really-smart-leaders