While the idea of a matriarchal society is at first glance interesting, it quickly breaks down in the light of WHY we live in a patriarchal society. Swapping the gender of the characters does not place Women in Men’s bodies and Men in women’s bodies it creates an entirely different person who learns and grows whilst under the influence of their gender and the biological impact it has on personality and development. For instance my fraternal twin siblings are an example of two completely different people, one male and one female, based on a nearly identical genetic template save for the addition of the Y chromosome with my brother. The Male version of Hermione would not be Hermione Jane Granger in pants just like a female Potter wouldn’t be Harry in a skirt. We live in a patriarchal society for a reason and that reason is based on biology. Men are stronger, faster and by nature seek to dominate their surroundings, women are by nature nurturers and do not feel the same drive or compulsion to dominate. The idea that you can flip the genders and have the exact same characters in the exact same positions within society is just not practicle. Case in point Malfoy. Since hereditary title is passed down through the male line, and has been that way since the Stone Age when male physical dominance was key, a female heir would have been unacceptable and therefore avoided.