Would be nice if there were some way to erode her support with those organizations, even a tiny bit.
Also, wouldn't pod pilots - as outside but in some cases decorated members of the Amarr hierarchy- be one of the few groups that are capable of being critical of the sitting emperor or empress. I would think that just as a matter of foreign policy if nothing else, in most situations the organizations that you mention have no choice but to show a united, supportive front.
Not to say that any criticism of the Empress wouldn't have to be tactfully phrased or risk even a podder being severely ostracized, but I think podders can exercise at least a bit more freedom in that regard than members of the organs of the Empire.