OK, but what about the (many) hedge funds that are volatile? There are indeed funds that are better than index funds, but they're inaccessible to the average person, and therefore irrelevant.

You're right, there are volatile hedge funds, although it might be accurate to say that there are more and less volatile funds than indices. Moreover, there are plenty of bad funds that only exist to dupe clueless retail investors into giving them their money. I wouldn't say that all hedge funds are good, and in fact regular people are probably screwed when it comes to picking a good one (in part because some hedge funds are what I like to call "20/20 funds" and are just statistical testaments to the fact that some fraction of poorly managed funds will still do well).

Volatility isn't a binary thing. Although the less-volatile more-return funds are out of reach for regular people, the less-volatile less-return funds are not, and these still have a lot of value for people who are less tolerant of risk.