Well to be honest I believe you underestimate humanity. There are way too many instances of clans who would fight till nearly both parties were eradicated. Regardless of that I am not convinced that is the root cause.

I feel this whole theory misses some key elements of our ancestors. First the idea that each male was able to reproduce at the same rate or had the same opportunity to breed as each other; this is not how nature really works! For most mammals only a few males get to bread each year with ALL the females in a herd. The alpha male will do the overwhelming majority of the breading for X number of years until displaced, i.e. dies of natural causes or is violently displaced. Our ancestors were most likely not very different. This, in my opinion, could be one of the reasons women in a group will synchronize their menstrual cycles, as it would help to ensure the male could bread everyone in a short time period and not worry about competitors sneaking in as much.

Also the idea that there were equal number of men and women needs to be looked at. Again, in nature, there is generally way more females then males. A healthy and diverse herd is considered to be around 70% female and 30% male.