This whole thing about the Fed Reserve being private is a red herring.
Yes, the Fed is nominally private. But the Bank of England was private for centuries until it was nationalised after WW2. All the problems remain there because the Central bank STILL EXISTS. It's the governmental powers that exist that are the problem, not who owns it.
You could focus on it being private and then maybe it would become a national issue and the govt would say "OK, we are going to nationalise the Fed". And if that happened, not one single problem would have been solved. The Fed would still be there doing the exact same as it does now, except it will have legitimacy in some people's eyes where it didn't before.
Your argument is a false dichotomy fallacy. You claim that our only choices are private or governmental regulation. Bitcoin is a perfect example of a third choice. He points out that the federal reserve is private to bring attention to the fact that the government doesn't really control it. Therefore even if you feel the government still represents us it has no power to change the policy of the fed. It could start using constitutional money again but that is another debate. Either way the fed does what it wants, or is replaced completely. The government is not able to dictate fed policy, and your statement assumes that we only have two choices.
His argument is sound. the ability of the government to give preferential treatment to one group of individuals over another is the crux of the issue and he makes no claims that we have only 2 choices.
Logically there is only one choice that is rational. No one group of people should have preferential treatment over any other group(no regulation). For this to work, you need Private Property rights otherwise you run into the Problem of the commons. People will arrive at the best solution by themselves... which seems to be, by general consensus... Bitcoin and crypto's in general...
whether or not it will stand the test of time like gold and silver has is another story though.