> many pension funds are not sophisticated, they're small, underfunded, and getting taken for a ride by expensive advisors

Who tend to come up with bumfuck benchmarks other than the common ones. Sometimes for good reasons. Often to justify their own comp.

> Many would be better off using an S&P 500 index fund

Maybe. They would probably be better off with some total-market funds (instead of biasing towards large caps, especially if they're small). But my point stands: pension funds don't tend to automatically follow any major index, much less the S&P 500 proper.