I think Laura is getting it right. Even though intelligence might help people increase their status in a vacuum, highly intelligent people tend to have other traits that might decrease their seeking of status or success at attaining it. It's a tradeoff.

For instance, many highly intelligent people are introverts, yet extraversion is probably an advantage for leadership. There is also a correlation between intelligence and openness to experience. While you probably need decent openness to be a good leader, you will seem wishy-washy if you have too much.

In certain fields that depend on competence, such as science, technology, and some parts of academia (but not others), status depends more an accomplishment and is more tightly linked to intelligence. In other fields, the most intelligent and epistemically-trustworthy people will have trouble ascending to leadership positions.