The Fed is technically a privately owned entity, which is really a caba of banks (banks in the US 'own shares' in the Fed and basically run the show). It's at arms length form congress - as it should be - for monetary operations.

But for regulatory issues?

The US let's a group of banks 'self regulate' - moreover regulate other industries?

The seems kind of crazy to me.

I see the need for 'smart regulation' esp. by bodies that are as 'independent' as possible, but in this case 'independent' could mean 'conflict of interest' which is kind of the opposite of what we would want, no?