the genuine reason why certain rich people don't act rich has nothing to do with status gains or zero sum games. There's plenty of rich people who do indeed act rich. Pick your favorite sports superstar.

The real difference is between new and old money. The nouveau riche like to show off because they're fixated with the idea that they've earned it themselves, very much on display among super rich techies. It's precisely the "non zero-sum" people who love to signal their wealth openly because they take it for granted that their wealth is based on merit.

It's your old money folks who have some sense of noblesse oblige who understand that wealth most of the time is indeed pretty zero sum and who think of flaunting wealth one as distasteful and secondly as potentially stupid if it attracts attention, which new money craves and old money does not.