[krapp]

>The thing is that if you are an established "alpha male" either in the hierarchical sense or in the sense that you are self-sufficient, there is little need to engage in intra-group aggression, and in fact that would likely be detrimental as others are more likely to want to strip you of leadership roles if you are violent to them.

The tribal and clan-based politics of most of human history would seem to disagree with you. It's only relatively recently, post Enlightenment and Industrial Revolution, that "alpha-male status" wasn't often established or leadership imposed directly through violence, albeit mediated through some kind of "code of honor" which usually only applied amongst nobles.

Look at classical literature. Who are the heroes? Often not merely poets, scholars or subtle artisans - but the men who carve their name out of the world in blood, the soldiers and warrior-kings.