The myth is so pervasive because it's propagated by people with more wealth against people with less of it, and the conflict of interest prevents anyone from giving it up.

Everyone wants to feel better about themselves and the easiest way is to look down on someone who has less. Less "whatever" really, people always find something that they think makes them better, money is just the obvious choice because society slowly associated money with success. It doesn't matter if the wealth came from their parents, or luck, they can still pretend it makes them better.

It's one of those situations where everyone's in on it. The poor really haven't much else to go on and they'll take this little boost in their standing, the rich are tempted to think they so much better than most other people. Everyone in between sits somewhere on that scale.