I work at an engineering company known for its fair treatment of women.

I disagree with you when you say that in the bifurcation between leadership roles and those being led that women are more likely to take on the latter role. If anything the women I work with are more sociable and hence more likely to want to manage rather than keep themselves in purely technical work. It takes all kinds. I for one am glad that there are men and women willing to take on management roles -- roles that I, for one, have no taste for.