Too often, a woman is shown to be subdued by her love for a man. To avoid this, generic powerful women (example, Lara Croft) is attached to no man, or is lesbian (example, Matoko Kusanagi). Because the stereotype is that no matter how strong the woman, true love would cow her and reveal a woman's true nature as meek and giving.
You should read Warrior Queens by Antonia Frasier (if you haven't). She lays out different ways real women have handled their powerful personae. And the archetypes are alive and well in the present culture.
And I think it's as much a mistake to underestimate the effects of our culture on us as to “blame” every bad thing that happens on it. But the biggest mistake is to act like it doesn't matter at all.