The flaw in the reasoning, the way I see it, is that they take a few examples (Facebook) and extrapolate them in completely unrealistic ways. It isn't reasonable that a handful of billionaires are going to replace the entire equity market, or even meaningful parts of it.
What you'll see is that eventually these private owners of Facebook will want to cash out, and when they do, they'll almost certainly turn to the public markets. That's what happens to most LBOs. Companies go private, and after a couple of years the investors want a return and they're back to the public markets with an IPO. I give Facebook 5 years, if they're still around by then.
Retired early, traveling perpetually.