To say that political power isn't influenced by gender misunderstands political power, actually.
First, physical power doesn't dictate hierarchy. If physical power needs to be asserted, then there is no hierarchy to speak of; the strong thrive and the weak perish. This isn't politics or hierarchy, it's simply primal, animalistic behavior - extremely primitive, evolutionarily distant behavior to say the least. And again, there's no necessity here, there's only the fact of behavior, which could be otherwise (female lions are stronger than male lions, for example).
Political power first emerged not through the assertion of physical strength, but through claims to knowledge and the ability to tell convincing stories - and gender is one such story. A physically frail or weak man could wield enormous power simply by presenting himself as the bearer of tremendous knowledge, and here we have an example of conflicting gender norms already: that masculinity is both wisdom and physical strength. Of course, early knowledge-bearers also saw the value in promoting physical strength, and so men and women began to find themselves cast in specific societal roles.
By the time advanced elections come into being, the role of social organizers and knowledge-bearers had long belonged to men. To say that gender played no role in this development is pretty myopic, to say the least.