On Piketty's second law

It is an asymptotic law : :Piketty’s Second Fundamental Law is not an identity or an approximate identity. It is, as Piketty makes clear at some length on pages 166-170 of the book, a long-term asymptotic law. For the benefit of the general reader, Piketty abbreviates the statement of the law in the form  “β  = s/g”. But it might be stated more carefully this way: “For a fixed savings rate s and growth rate g, the capital-to-income ratio β converges over time to s/g.” He might have abbreviated it in more conventional fashion in the form β → s/g. Piketty sketches an elementary proof of this convergence theorem in his online technical appendix. Like any limit theorem proved over the real numbers, it requires implicit restrictions on the range of the variables to avoid singularities."
Dan Kervick has written more about it in an earlier post. Piketty explicitly says that it does not explain shocks "but it does allow us to understand the potential equilibrium level toward which capital/income ratio tends in the long run, when the effects of shocks and crises have dissipated", page 170. He goes on to discuss this factor (as well as others like privatization) for the increase of β after the shocks of the wars (page 187 onwards).
Anyway this law seems to be drawing some criticism from various sources.