I think it's because they're still living in a patriarchal society and she's an outlier. Most women are still seen as home makers and that women still think that's their role. She inherit what she have because her family is from nobility and I think most women would think it would be more of a disadvantage if there's no name and power to back them up. It's not really unheard of, especially women in power back then. Even having a woman that wields all the power to rule over them, it really doesn't change the fact that patriarchal and stereotypical gender role is so deep rooted but that's my opinion
Let's take Queen Elizabeth for example. She's the virgin queen and is the most powerful monarch in Europe during her time. She holds more power than men but even then women are still tied to patriarchy and stereotypical gender roles because they know they don't have the same absolute power like the queen. How much more Asha who's only a Countess. It's not easy to deconstruct patriarchy, gender roles and misogyny that it comes with especially if it has been established more than Asha was born and Asha doesn't have that in mind as you can see, you know, making women equal to men. She's even seen as barbaric because she's a woman and treated like a wild animal when she first went to the kingdom. Her priorities is the safety of her people. It's easier said then done. If there are women like her there are only a few and not common place.
That is a good take BUT she was at the CENTER OF POWER. The Count of Pervas isn't, they are at the fringes barely even in the same kingdom.. they are smack at the edge of the border.
They were essentially banished to a region that was inhabitable before them. If there was strong misogyny as you suggest, The Original Count of Pervas would have insisted and married Asha off so as to secure their bloodline.. he did not. None of her brothers even suggested it (they would have implied if it was so)... Nobody even brings up the fact that she is a woman IN FACT they do not care.
If you see how the region acts, you'll notice nothing as "forced" roles. People are there by their choice and just try to survive. I highly doubt if any woman indicated about joining the army and had skills that they would have refused.
... I guess I understand why the Author is trying to make Asha this selfless person and super strong, but all I can think of is WHY there isn't another woman in the army.
If you think about it logically, it doesn't make sense. These people were banished with their families to the North to fight, am I to believe none of them gave birth to girls and the few that did? none of the girls wanted to be a soldier like Asha?? nah,I do not think so...
Just imagine how cool it would have been if there were females in the army and only the North did this and they have equal rights to do whatever cause everyone fights in the war for the Empire...