The challenge of Durlauf to Piketty, in context

The mild criticisms of Steven Durlauf, editor of the Journal of Economic Literature, to Thomas Piketty in two debates in New York and Chicago would not lead one to anticipate the very tough review by Durlauf and his co-author Blume published in the Journal of Political Economy of the now famous book "Capital in the Twnety-First Century," by the French economist. The critique of the book has several fronts, including data, theory, policy, and the overall "methodological" approach of the book. The theoretical criticisms are to some extent already present in the reviews by Lindert and Milanovic, among others. This is not my field of expertise, but they point to the theoretical difficulties of making predictions about inequalities of personal income based simply on the rate of return on capital and the growth rate of the economy, as Piketty does. Blume and Durlauf's theoretical criticisms go beyond these macroeconomic issues and expand to the theory of justice ("lack of serious engagement with political phylosophy"), pointing out that there is nothing in the existing theories (both traditional and more recent such as in Sen or Roemer) that justifies basing a policy framework on claims about the 1 or 10% of the population instead of the other 90 or 99%. The data criticisms of Blume and Piketty have several fronts, but to me the most important one is the lack of consideration in Piketty's work of data on the distribution of welfare coming from the consumption of public goods. The criticisms on policy are basically about how Piketty neglects policy instruments against inequality that could go beyond taxation, such as political reforms that could reduce the weight of the rich in politics. But they also challenge some of the specific prescriptions of Piketty on some of these non-tax issues, such as policies on education financing. The reviewers dismiss the supposed erudition of Piketty that has been praised by some of his admirers, for example by blaming him for not being systematic in using literature as an evidentiary source (footnote 10 of the review, p. 755), and by writing that "when Piketty moves to topics for which he has not done original research, he is careless with theory, and empirical evidence is presented in an unreflective and selected fashion."
I have to say that I came to know the work of Durlauf very recently. His name just sounded familiar to me until I started reading his papers about complexity and economics, and about social capital, which are excellent pieces of scholarship and criticism, in my modest judgement. He and his co-author Blume claim to share the liberal (progressive) values of Piketty. So do I. Then, what does survive of Piketty after Durlauf's attack? In the view of this blogger (who has shared in the enthusiasm of seeing a book on inequality becoming a global best seller), a few important contributions still survive:
-The existence of strong inequality trends, derived from Piketty's and his co-authors research on top incomes from fiscal sources.
-Policy intuitions about the need to use policy instruments and institutions that go beyond the nation-state (like international taxation), which go beyond Acemoglu and Robinson in spite of Lindert's attempts to call for a synthesis in his review. Although Piketty himself downplays the importance of the fourth part of his book on policies, perhaps it will turn out to be his most enduring legacy.
-The need, as Milanovic claims (mentioning Freakonomics and "randomistas") to ask important and not trivial questions in economics, even though the answers should be more qualified (especially if Steven Durlauf is reading).