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.
Not really.
Maybe "flunking your way through" would be awkward, but these folks know the easy majors. See Government at Harvard. See W's surreal academic career for an example of a well-connected but relatively unintelligent person get a Yale undergrad degree and a Harvard MBA.
However, for most of the mere mortals at Yale and Harvard, they still have to compete with the every other college graduate, and some of those other college graduates are pretty smart themselves.
because someone is paying good money for that "A"