That logic doesn't hold if every generation of parents has their parents raise their children. You get to have your kids and have your parents do a lot of the hard work. Then when your kids have kids you become the primary caregiver.

Regardless of whether everyone has their parents act as their children's caregiver or whether they act as their own children's caregiver as long as every generation does the same you are only primarily responsible for raising one round of children. Its just a matter of whether you do it when you are younger or older.