Privilege has its limits. Let's take your example. If you're inheriting Dad's investment bank, you still have to keep winning their clients. Most institutional investors have policies which require them to freeze and reconsider firms after leadership changes. If you flunked your way through Harvard, that's going to be difficult.
More often, Dad doesn't own the investment bank. He's a senior officer there. This, again, confers some advantage. But outside of inheriting an estate, there are lots of controls prevent blatant nepotism.