As for the argument, it seems to me we're talking about complex interplays of sex and status, and, as far as politics is concerned, the special degree of status that is spectacular celebrity. That women are willing to pay more for a haircut than men (and less for a car) may have apparently little to do with equality, but when that sex/status competition formats political representation, I'd say it clearly does.
I said sex/status competition as currently magnified by celebrity pressure in the political arena poses a problem of gender equality. How's that?