The choice to stay home and take care of the kids is often the
partnership's choice, not just the one spouse's. For instance, sometimes the cost of hiring childcare is more than the parent's earning capability. So out of economic necessity, one person stays home to take care of the kid (let's call this person, "the mom"
-- but of course it could just as easily be the dad).
So The Mom, for the benefit of the Partnership, takes on the more than full-time job of child care, and whether it's her preference or not, her value on the job market is stunted. Ten years later, a divorce happens -- the partnership is no longer working for either or both of the original partners, let alone the newer recruits. The dad's earning power in those ten years has grown. The Mom has in the meanwhile been economically devalued, but for ten years she has contributed to the inherent value of the partnership, providing real and actual support to the Dad and to the Kids. Ideally, she will continue to provide value to the Dad by supporting (in ways other than economically) their kids until she dies. Although the Partnership has been terminated, the effects and responsibilities of the partnership continue. Just as her responsibilities, the ones that were put into effect by that old partnership decision, continue long after the marriage ends, so do the Dad's -- the old decision impacted the entire family and continues to do so. The Dad, by helping the Mom financially after the marriage ends, is acting in good faith to support the well-being of himself -- by supporting her in supporting her kids in the non-economic ways. A family doesn't stop operating, and all the choices made during a marriage, don't become instantly invalidated because of a divorce.
And I'm not saying The Dad should pay the Mom's bills for the rest of her life. I do think he has a responsibility (and it's in his and his children's best interest) to minimize the negative effects she incurs in the marketplace because of the old decision made by the partnership. They're still a family.