if you asked a group of people to rank the status of a bunch of businessmen/athletes/janitors based on one photograph then their responses would correlate better than chance.

That's an interesting experiment to suggest, let's think it through carefully.

Suppose we took a set of photographs, each of a single person, in a similar pose, and we asked a random sample from a given demographic to rank these photographs.

Immediately one complication that arises is what question we're asking. "Rank these people by status" is going to be interpreted differently by different people creating one more variable to control for: any correlation that arises could be a correlation in how people in our sample are likely to interpret the question.

Even supposing that complication could be somehow mitigated, there is the question of whether people are basing their rankings on some readily available characteristic other than status. It seems likely, for instance, that irrespective of the question asked people would perceive physical attractiveness (which is but one form of "influence power" as the post uses that notion) and rank the photographs according to that.

Intuitively, I wouldn't necessarily expect that if you controlled for physical attractiveness, there would be anything left for people's rankings to correlate on.

But the post is quite clear that physical attractiveness is not necessary to achieve what people would call "high status", any more than starting out wealthy is the only possible way to acquire a house (we have an existence proof that you can do it with one red paperclip to start with).

a different set of questions, which, while valid, are not the questions that people usually ask about status, and which I think miss the point.

Perhaps it is "the questions that people usually ask about status" which miss the point.