I have done a lot of research on this and I am still on the fence on this one as there is evidence of this going back long before the 2nd century. Now it may not have been written down before then, however, there is evidence of it being practiced. I tend to lean towards the fact that is the mother who has the first influence in raising a child and therefore, if the mother is a practitioner of the Talmud, then the children will also be raised as practitioners of the Talmud, following every man-made burdensome doctrine of the rabbis.
I agree with what you say. A lot of what was codified had been previously in practice. Part of the oral tradition. As a democratic country, committed to equal rights for all, we can revisit the gender stereotypes. But, we do not raise up women by putting down the traditional roles of women.