I agree with much of what you've said, except for this part, which is true, but only in the West in the relatively recent past. Besides the Aka that I mentioned, where men spend just as much time holding and bonding with new born babies as women, many anthropologists believe that early humans engaged in alloparenting (group parenting).
“Years before a mother’s previous children were self-sufficient, she would give birth to another infant, and the care these dependent youngsters required would be far in excess of what a foraging mother by herself could regularly supply. Both before birth and especially afterward, the mother needed help from others.” (p. 31) Without alloparents (kin and others besides the actual parents) to help feed and protect them, few Pleistocene children could have survived into adulthood."
Often alloparents were aunts and grandmothers, but also male kin and "as kin" as well. The idea that mothers must be the primary caretakers and spend all of their time with children because that is what is "natural" is largely a function of patriarchy, which only a arose a few thousand years ago. The erroneous belief that the nuclear family, made up of both a mother and a father who are married to each other, is the ideal environment for raising a child, has caused no end of harm to families with different configurations (such as same sex parents).