Female pronouns are also used for your country, for example, so it also has that "mother" connotation, probably passed down from the original "Mother Earth" godess that has been so carefully almost removed from the Bible ... ( " ) Except for Germany, for some reason, which calls it the Fatherland.
I think we start to uncover the psychological fault lines in our early societies when we talk about the role of women: mother (of me and of our children), virgin, whore, etc; it demonstrates that no matter how expert a female person is, they ain't never going to live up to the expectations put upon them because they are -- at least partially -- mutually exclusive.
Also you are saying that the feminine gender pronouns necessarily equate to the subordinate of equivalent masculine term. This may be the case, but I would argue it has more to do with the cultural mores than any fault with the language per se, and so the idiom can be remedied by a substantial application of effort and time! So that eventually an aviator can only ever be a pale imitation of an aviatrix ...
What did the Amazonians call their officials?