The issue becomes what is "best educated" and who gets the opportunity to be "best educated". Drawing from a narrow circle of people is problematic. It leads to a form of systemic 'group think'. Social homogenization leads to static dysfunction. Egalitarianism is not just about fairness, it is about the instrumental value of diversifying and refreshing leadership in terms of backgrounds and experience. 

I do suggest you read David Halberstam's "The Best and the Brightest", an excellent account of how the boys from Harvard and other Ivy League schools led America into the disaster of the Vietnam War.