As an Assistant Residency Director at Harvard, I often heard my colleagues ask, "Will she be a leader?" or "Can we count on him to show leadership qualities?" when we discussed applicants.
But maybe being a leader or even an extrovert is not what we should be seeking in all applicants. Poor leaders can bully, be arrogant, and may ignore excellent advice. In academics, I saw many leaders who were not role models in their behavior or scruples.
Here's an interesting New York Times piece about the need for introverts and even followers in college admissions. I found the story about the young woman who tried to overhaul her personality and activities to fit the admissions mold to be particularly telling.