The whole demographical transition to lower birthrates has a more detailed explanation in the theory that more educated women are much more choosy and (at least) less enthusiastic with bearing children with men of about equal status. UN data says that we just reached peak baby, with significant exception in Africa only, where prospects for improving status, the living standard or marrying up are still well believable.

So instead of children per woman decreasing evenly, you would have one group of women continuing having many children and another ot having any? Right?

Sounds totally off base to me, but it is a testable statement. Now go see if you can find data that supports your statement.