I mean if we want to be more logical and rational, the old culture should have been a polyandry instead of a polygamy because women were saw as weak and the reason why they were given to just one man.
Of course, if the male heir was from a rich family, having many wives would make sense because they would have more kids and a high success to have an actual heir. We have to remember that many time women died in child birth because of the poor hygiene and malnutrition BUT it would have been better a polyandry.
My reasoning behind this is a single woman in the family would be well protected by the husbands, a portion of husband would stay behind yo protect the house while the others would go hunting and take care of the farm that the woman taught them how to. It is natural to see women staying closer to their family. That would have increased the number of men protecting the matriarch house since the daughters would bring the husbands and help the parents.
Since the wife didn't need to fight over who clean and who will cook since there are more husbands and servants, they wouldn't go thru emotional roll coaster and maybe hygine part would have been discovered sooner. We saw how female nurses were the one to pay attention in minor details (lucky or unlucky most females have that tendency to pay attention to details. Another reason why most can see different type of tones of the same color. That is how, in average, female brains work)
It makes me wonder who was the rich dude that made it so that patriarchy would become the norm. Men wouldnt be fighting over who is the father since the only bloodline that the group would take care of is of the wife. Having many husband to satisfy, would make it tiredful for her to cheat on them. I mean sure look for another husband but after awhile it would be too much work.
While in the patriarch lineage we see many men dont even touching their many concubines after their first night cuz they have their favorites already and only accept more women to keep a good relationship with the neighbors