The question I have, what problem are your suggestions designed to fix?
"at a minimum the Comptroller General should have the power to audit member banks without written permission in advance from the Fed."
What conspiracy has been uncovered that this would prevent? I know of none. At the same time, I know of dangers of "audits" by the government: they begin on paper and end with night visits by secret police (yes, laugh all you want). The Reserve banks are a coalition. You don't want to be a part of it --- stay out, whether you are a government or a private citizen. And here lies the crux of the matter: with all the suspicions you and I may have about coalitions (and vigilant we must be), there has never been a better system in the history of the world. Small private citizens lack sufficient capital. The alternative is the Government itself. And that has always been the problem: as Hayek well pointed out, once the economic freedom goes, the rest of the freedoms follow.
"I also think the Comptroller General should probably audit discount window operations, the reserves of member banks and interest on their deposits."
All this is public knowledge. The Fed publishes its balance sheets periodically. If there were some kind of anti-social activity, it could exist for no longer than one period. What is the benefit of speeding this up? Questionable, if any; but the dangers are numerous.
I understand your position much better now; thank you.
Friedman and Schwartz disagree with you on that. Before the Federal Reserve Act financial panics in the US were mitigated by the actions of private commercial bank clearinghouses. The Fed took over the role of the clearinghouse associations particularly the lender-of-last-resort role, did less to mitigate the panic of 1929 than the private associations had done in earlier panics like 1907 and 1893. Their point being that the economy would have been better off if the Fed had not been created. Without the Fed the Great Depression would have been just another panic and recession.
I know people like Paul Krugman disagree. I also know that there have been and will be books written taking one side or the other, so you and I are not going to resolve the question of who is right.
I do appreciate your thoughtful responses and thank you for sharing you knowledge on the subject. I’m going to have to study more on this