In 1983, the organized Reform Jewish Movement adopted the principal of patrilineal descent. Reform Judaism considers a child of an interfaith couple to be Jewish if one parent is Jewish and the child is raised as a Jew and receives a Jewish education and celebrates appropriate life cycle events, such as receiving a Hebrew name and becoming bar or bat mitzvah.This also assumes that the child is being raised exclusively as a Jew and not practicing another religion.
The "maternal ancestry rule" was instituted by later Rabbinic authorities for political and religious reasons (the Jewish exilarch Bustenai, for example, had no qualms about taking a Persian wife.
Historically, since the Rabbinic period (post 70 CE), Jewish status was passed down by the mother. A child of a Jewish mother is Jewish, even if the father is not.
Prior to this period, the Bible recognized patrilineal descent, whereby one’s Jewish status was determined by one’s father.
We also see numerous instances in tanach of Jewish men marrrying non-Jewish women, however we see very few examples of Jewish women marrying non-Jewish men and when we do, it is usually referred to in a negative context. Assuming everything you wrote about history is correct, these Jewish men took non Jewish women for wives and they acted as Jewish wives.
A quick glance through tanach (particularly the story of Ruth) would indicate that the current geirus process is completey superflouous and even anti-Torah. They adopted the ways of their husbands because that was how things were done.