Failing to diversify is the fund managers' problem. Pension funds shouldn't have all their investment in a single countries' stock market (doesn't matter that most, if not all, of those companies operate worldwide, they are still from the US), not even in equity markets. A wiser investment manager (or individual investor) would put a chunk in different kind of equities, and diversify into fixed rate, precious metals, perhaps real estate... Not bet it all to the volatile S&P 500. "Past performance does not guarantee future results.".

What’s the mechanism you have in mind for that happening via bubble? They sell early before the crash? I’m curious if that actually happens, since the mass psychological nature of market crashes seems to make them difficult to predict reliably, even for people with a lot of resources.

Inflation on the other hand definitely does reallocate real value to whoever already owns a lot of assets, and I believe inflation often goes along with bubbles, since credit expansion is what usually kicks off the bubble in the first place.