Because if you're not born rich your chances of dying rich are astronomically low. We pretend social mobility exists when in reality it does not, or at least it's extremely rare (even in the US, now more than ever).
I think the problem is the flipping from "Billionaire" to "rich". To get to the most insanely abnormal outcome imaginable, you need crazy good conditions and lots of luck. To get to the level of "rich", by most people's standards, you don't need anywhere near the same level (though of course, luck still plays a role depending on how you define luck - I mean in some sense, you're crazy lucky to even be alive given the odds against the particular sperm/egg matching that made you up.)