A person is promoted until failure. All else being equal, if two people are leaders, leader A will be on average as good as leader B. If one were significantly better, they would be promoted to the next level - eg a retired philanthropist billionaire or enlightened monk or what have you.
If P and Q are qualities correlated with leadership, if P and Q are independently randomly distributed, then a leader with higher P is expected to have a lower Q.
An analogy: farmers who grew 2 truck loads of bananas meet up to compare farms. On average the farms are 4 square miles. If farmer Joe tells you his farm is half a mile wide, you might guess it is 8 miles high, because the area is expected to be average. There was no causation at work — having a half mile wide plot did not cause the plot to be 8 miles tall.
Why should we assume that there is a causal link between high iq and being disliked, when it could be chalked up to correlation between factors of an equivalence relation? High iq allows non-charasmatics to function higher than they normally would, just as charisma may make up for a lack of brains.