Here is the part I'm referring to

Yes, and how does it show that "it's not clear that the food provider role of males was actually widely present in prehistoric people"? The observation that women "work hard and move around" does not support the notion that they can feed themselves and their kids without any help from males.

I'm trying to argue that it's not clear at all that considerations whether or not to have sex are genetically determined by other things than physical attraction.

I am not sure I understand. Are you saying that the only genetic imperative for males is to fuck anything that moves and that any constraints on that are solely cultural? That's not where you started. Your initial question was:

But how significant is the 'traditional' male father role for a good upbringing of a child?