My theories:

a) most people achieve social capital through relationships. Rich people gain it by distinguishing themselves among their already distinguished peers. Even if being obnoxious is what’s making you famous, you’re still more famous than anyone you know.

b) The cadre of rich people you’ve actually heard of self-select for craving attention and validation. Like most people, they aren’t good enough at anything to be famous organically, and like many of those people, are also insecure about their profound lack of specialness. But, few people have the money to buy the attention they crave.