At its base, Judaism is a patriarchal religion. Irrespective of our post-modern insights into the role of women in the Tanakh, in rabbinic literature, in Jewish history, Judaism was constructed on the idea of separate spheres. It's encoded in our ontological literature (heaven from earth, firmament from firmament, light from darkness) and in our rabbinic literature (holy from unholy, sacred from secular, kahal from ki avi). In all of our source material, a clear distinction is made between the spheres in which a man operates and the spheres in which a woman operates, the laws a man is bound to uphold and the laws a woman is bound to uphold. Furthermore, regardless of our history of strong female figures, our religion is patriarchal from its roots. Our God takes exclusively male nouns (I do not buy the neuter argument), the majority of our prophets were male, the priesthood was a male trust, and the rabbis are all men, all dictating the religion. Instead of going into the social, historical, and theological minutiae to explain why our religion and social structure were thus constructed, I'll point you to the brilliant Tikva Frymer-Kensky (z"l), whose prolific work on this subject far outshines any attempt I would make to do the topic justice.
Any conversation we have on women’s roles in Judaism must take the fact of Jewish patriarchy into account. Inserting the emahot (matriarchs) into the Amidah does not actually address the issue of separate spheres, it provides a gloss that makes us feel as if we are addressing the issue.