It is dangerously tempting to think that way - "He is high status because he is good at seeking status, rather than being intelligent" which sort of implies "I am low status because I am intelligent, rather than being good at seeking status".
cf. Nietzsche's master/slave morality.
Or the two are fairly independent - you can be good or bad at seeking status, intelligent or not-so intelligent, and it is possible to have any combination of those, including that of being unintelligent and yet still good at obtaining status.
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: