> Moral of the story: rich people will always want to show off that they are rich.

I think you mean, "Some rich people are insecure enough that they want to show off that they are rich."

Amex caters to this very well: they play the whole "prestige" thing but if you have a "higher-level" card for the benefits (platinum, black) they are happy to issue you an ordinary green one you can use so people won't guess your wealth.