I forgot
In the above scenario adultery would also become a criminal offense. If a man can have more than one wife he has no need to play the field and if he can get another wife the one he has should be motivated to perform.
Yes that is crude and venal but that’s life
It had its definite downsides among the tribes and not just the first wife making life a living hell for second wives and beyond. There were cases where rival wives actually killed each other.
Typically, the maximum penalty which could be imposed for such a murder was banishment from the tribe. More often the murderess got off far more lightly by being beaten, having her hair shorn and being forced to sleep outside the teepee for the couple of months or so it required for her hair to grow back.
But more often, they adapted and the Alpha wife, so to speak, enjoyed the help with the household chores far more than she resented sharing her husband. There were also efficiencies from division of labor-- one woman might excel in child care, another in making clothes, a third in food preparation, etc. A man who could organize his wives in such manner might become quite wealthy by tribal standards.