Have the Danes rendered families less important?

From Tyler Cowen.

"Many American policy analysts point to Denmark as a model welfare state with low levels of income inequality and high levels of income mobility across generations. It has in place many social policies now advocated for adoption in the U.S. Despite generous Danish social policies, family influence on important child outcomes in Denmark is about as strong as it is in the United States. More advantaged families are better able to access, utilize, and influence universally available programs. Purposive sorting by levels of family advantage create neighborhood effects. Powerful forces not easily mitigated by Danish-style welfare state programs operate in both countries.

Here is the full paper by James J. Heckman and Rasmus Landersø."