Your blog is interesting and useful. Piketty is addressing an important issue but the book has serious flaws. The comment about parasitic critics reflects a devotee of the cult of Piketty one supposes.
Piketty makes some strong and implausible assumptions which drive his model. Krusell and Smith as well as others have made this point. (Sorry I have not read all the critics cited above.) When growth falls, investment explodes leading to immiserising growth with all income flowing to capital. This is contrary to most economic growth models where if growth falls then investment falls perhaps with a lag.
Over the period since the mid 1980s inequality has gone down on a global level as hundreds of millions have been lifted out of poverty in China, India, Indonesia etc. See the articles by Milanovic. The pattern of the last three decades has been convergence between rich and poor nations. It is not clear to me why Piketty assumes that convergence will stop in the decades ahead. In fact the evidence of the last three decades is that globalisation reduces global inequality despite rapid expansion of the world population.