Thanks for focusing attention on the question, Will. Let me, though, challenge your analysis.
The fundamental question is whether equity investments made through private (illiquid) markets provide better risk-adjusted returns than equity investments made through public (liquid) markets. Your essay doesn't even ask that question, much less answer it. The quotation from Ted Eliopoulos, for example, says nothing about risk-adjusted returns: I can achieve net total returns of 7 1/2 percent using absolutely any asset whose returns exceed the cost of capital, simply by adding enough leverage (and therefore risk). That seems to be what private equity has "achieved" for approximately the past 20 years.
Likewise, your comments about the largest companies' share of public market cap in various markets are irrelevant: "the most exciting components" depends entirely on whether the BEST investments are in public or private markets, not how big the biggest public companies are.
CEM Benchmarking, in a study of the ACTUAL investment results of more than 200 large U.S. pension funds over the 17-year period 1998-2014, found that the Sharpe ratio (risk-adjusted returns) of private equity investments was 0.32, which was exactly the same as for U.S. large-cap stocks and less than the 0.36 for U.S. small-cap stocks. And that wasn't taking into account the additional risk of illiquidity. (The report, which my employer sponsored, is available for download at http://www.cembenchmarking.com/Files/Documents/Asset_Allocation_and_Fun…; see especially table ES5.)
Lots of independent academic researchers have evaluated whether private equity has provided better investment results than similar investments in public equity, and they have had a very difficult time showing any advantage.
Investors in private equity have taken on a huge amount of risk, and it's very far from clear that they've been better off as a result.