Many people make the claim that the fundamental problem of the US is wealth inequality, or no social safety net, or disdain for the poor. I believe these claims are much more common (and in my opinion could be considered more fundamental) than the claim that nepotism is the fundamental problem.

Well, symptoms of problems tend to be more evident than their root cause, so commonality of claims is not a particularly good reason to rule out nepotism being a problem.

Evidence would be nice to have though.

As for me, I've had enough anecdotes to think it's plausible. Just recently we hired a new CTO at my company, and he got the job simply because he was friends with our CEO and he needed a job. Turns out he's completely incompetent...