" Some had very impressive careers, but when you realize that first opportunity was only because of a parental connection, suddenly it seems a bit hollow."

Frankly, that sounds depressing. Seen like that, people who were born to wealthy parents have no way to prove their own quality. They will always be suspected to be just lucky and riding the easy wave.

"then you can simply not fuck up"

There is nothing simple about that. I consider myself fairly smart and I fucked up royally several times in my life. It did not destroy me, I was able to put the pieces together, but none of the decisions seemed bad at that time, either to me or to people I consulted it with. There is a lot of traps out there.