I think the "absentee father" issue would be easy to address: have the courts stop favoring mothers as custodial parents in divorces.

Of the divorced couples I know with children, the mothers were awarded custody in every single case, often over the strenuous objections of the fathers and other family members like grandparents (and in one case, even in the face of documented abuse by the mother).

I feel like studies on the effect of children who grow up with a missing parent need to somehow control for couples who split because of mental health issues. Otherwise, it's studying not the effect of the absent parent, but the effect of the behaviors of the parent who was granted custody, and some of those behaviors may strongly correlate with not being able to maintain a marriage or other partnership.