High status people are usually trusted with status because their methods/opinions match those who follow them. The pace of change-of-opinion will be slow for followers who have too-high a dependence on the authority of status.
High status people need only to be "effectively" stupid: you are compelled (whether or not you are stupid) to match the pace of change of those who uphold your status, as long as you value your status. Others who are more "effectively" stupid will usurp your status, if you exercise your intelligence and publicly abandon those who are dependent on your authority.
Michael Vassar once suggested: "Status makes people effectively stupid, as it makes it harder for them to update their public positions without feeling that they are losing face."
To the extent that status does, in fact, make people stupid, this is a rather important phenomenon for a society like ours in which practically all decisions and beliefs pass through the hands of very-high-status individuals (a high "cognitive Gini coefficient").
Does status actually make people stupid? It's hard to say because I haven't tracked many careers over time. I do have a definite and strong impression, with respect to many high-status individuals, that it would have been a lot easier to have an intelligent conversation with them, if I'd approached them before they made it big. But where does that impression come from, since I haven't actually tracked them over time? (Fundamental question of rationality: What do you think you know and how do you think you know it?) My best guess for why my brain seems to believe this: I know it's possible to have intelligent conversations with smart grad students, and I get the strong impression that high-status people used to be those grad students, but now it's much harder to have intelligent conversations with them than with smart grad students.
Hypotheses:
Did I miss anything important?
Having achieved some small degree of status in certain very limited circles, here's what I do to try to avoid the status-makes-you-stupid effect: