I may be misunderstanding your point, but I certainly don't think it's true that institutional investors are increasing their holdings of illiquid assets because of their long-term horizon.
For example, the measured volatility of illiquid assets is less than for otherwise-similar liquid assets when measured over short investment horizons such as a month, quarter, or even year, but not when measured over the longer investment horizons that many institutional investors SHOULD be using.
Similarly, the measured correlation of illiquid assets with liquid is relatively low when measured over short investment horizons, but not when measured over longer investment horizons.
These patterns are called a "downward-sloping term structure of volatilities" and a "downward-sloping term structure of correlations." They arise in part because returns of illiquid assets are measured incorrectly over short horizons, but those return measurement errors tend to be corrected over longer horizons.
For an example of the downward-sloping term structure of volatilities, please check out http://www.slideshare.net/casebrad/volatility-and-risk-adjusted-returns…,