I think you have this pretty backwards. Private equity does not exist because of pensions. Private equity is investment that has not taken additional steps to be a part of regulated public markets.
It's true that private equity is dominated by institutional investors. One reason for this is that the investments are generally deemed too complicated, illiquid, and risky for retail investors (although the Trump administration is trying to change this).
Additionally, if we added the kinds of regulations, reporting requirements, standardization, etc, that would be necessary to scale this model to hundreds of thousands or millions of investors participating in an informed manner, we would simply recreate public markets.
Freakonomics recently did an episode on this that I thought was pretty good: https://freakonomics.com/podcast/is-the-public-ready-for-pri...
They've done some pieces on private equity in the past too: https://freakonomics.com/podcast/are-private-equity-firms-pl...