> One time out of five, the consequence of that investment strategy is 'The market had a crash and I lose everything'.

Which is why that strategy doesn't actually beat the market. Keep using it for 30 years and you're bankrupt.

Whereas if you put your money in a major index 30 years ago and left it there, or even 50 or more years ago, what result? Are you even in a bad place if you put all your money into the market in 1926 and left it there for 100 years?

Yes, if a retirement fund had put all their money into a stock index in 1926, it wouldn’t have been able to pay out pensions throughout the 1930s and 1940s and would have been bankrupt before the market eventually recovered.

Going full index is a great strategy for an individual person aged 20-50, but not a strategy for a pension fund which needs to continuously pay out.