A secret misogynist agenda
Let's look beyond the immediately obvious Extraordinarily Empowered Action Girls
for a moment, shall we. In the series we are told that antigens created on contact with sperm will create antibodies that disintegrate the Nanomachines
. This leads to the question: Why such a Weaksauce Weakness
? Before we go into the Wild Mass Guesses about how this vulnerability actually plays out, we should note that sexual domination of women was once - and in some quarters still is - seen as a mark of masculinity. For the more so-called pure amongst us, it is also worth noting that the semen-covered woman is a recurring motif in pornography, a "genre" that for obvious reasons has been called exploitative.
A second point may be made that it is only women who are shown to be Otomes. In most cases, except for one prominent exception, the heads of state these Otomes are attached to are men. This fits with the picture of women being subservient to men. You note that, with the exception of Midori and Rad's crew, there are almost no men being commanded or led by women.
It may be safe to conclude that there was a misogynist agenda at play, or if not then we may concede Unfortunate Implications
First, about politicians. If anything, the Earl political scene is more female-slanted than the real world. Let's see: Mashiro, Yukino, Fumi's unnamed master (S.ifr), Midori, not to mention the leaders of Garderobe: Fumi, Una, and Natsuki, and the latter two are portrayed as strong-willed and no-nonsense. The Five Columns have surprising political influence too: Mahya basically bosses the Emperor of Carlteya/Cardair/Chaldea/aaaargh
around. The four major antagonists (Nagi, Sergay, John Smith, and S.ifr John Smith) are all male. Of the three factions with access to advanced technology, the "good" Garderobe is all-female while the "bad" Schwartz seems male-dominated, and the "neutral" Aswad is a mixture of both.
As for the Otome being subservient to political leaders (of both sexes!), I suppose you can dig a Stay In The Kitchen message there if you squint just right, but nobody says the current Otome system is a good thing. It's portrayed as a mixed bag at best, and the major characters' opinions on it range from "necessary evil to prevent wars" to "down with the Otome!" Sunrise does seem to have thinly-veiled agenda there, but it's more about WMDs than gender roles. Note also that while the Otome are subservient to the rulers, in their countries they still hold positions of great influence ? Haruka, for one, is a Brigadier General leading a mostly-male army