To take an absurd example, say there's a 50/50 chance of going from rags to riches. That would mean half of the bottom 10%, 5% of the population would move up to the top 10% of the population. And somehow the middle 80% don't manage that feat. You would expect the probability of going from the bottom to the very top would be low. Instead, the article tries to paint a negative picture. It points out there's a 32% chance a child born in the bottom 10% will stay in the bottom 10%, when you could just as well point out that child has a 68% chance of moving out of the bottom 10%. Bringing in statistics about how many of them move from that percentile to the highest percentile obscures rather than clarifies the issue of income mobility.
Then there's his universal welfare idea, which at $250,000 per person and a quick back-of-the-envelope calculation would only cost about 56 trillion dollars. Plus another 2 trillion or so per year with population growth.
That said it's worth reading, the “individual development accounts” idea is definitely interesting.