I, too, am dubious about Pikkety's thesis. But I'd like to call out a distinction between the concentration of wealth, and the static nature of the oligarchy. One will continue to happen, the other Pikkety could be dead wrong about.
Andreessen says (paraphrasing) in the interview, 'Pikkety says wealth and oligarchies will happen, but look at the Forbes 400 and you see lots of churn, where is this supposed stability that will happen with rich people cementing their gains'.
It's true that Pikkety presents a view of social mobility becoming increasingly static, and reverting to a supposed historical norm.
But one lovely book I have pg to thank for reading, "The World We Have Lost", talks about how things were in England according to an analysis of actual data (county records etc). One chapter, 'The One-Class Society' ('gentlemen' were the class, the only class that mattered), speaks of how there actually was a large amount of 'churn' in the gentleman class -- even outside of cities and the merchant classes, it was possible for a father to become a substantial yoeman, and his heir to become a gentleman. Families went up, families went down.
But despite a certain amount of mobility being possible, all effective wealth and power that mattered was still very concentrated, as it has been for much of recorded human history, for many reasons.
This was momentarily interrupted by the usefulness of humans as wet robots that were briefly able to exert the political and economic leverage necessary to drive hard collective bargains about their compensation.
That was temporary. (Offshore wet robots, and eventually dry robots, taking the place of the less-needed troublemakers).
Wealth, even if mobile, will inevitably become more concentrated due simply to better technology and efficiency -- how can this not be so? It seems self-evident.
So, I guess the question is:
If technology magnifies individual differences in productivity, and if we accept as a given that attempting to tax away the resulting fruits of that productivity is on the whole economically injurious to an economy, how can wealth not become more concentrated over time?
(Yes, of course, there will be churn and disruption, and wealth will change hands. Even as it did among the gentleman class in England in the 1500s; families came up and families went down. But because of technological magnification of productivity it should tend to go to fewer people. This just seems like a natural law.)