What Monetary Policy Cannot Do

Casey Mulligan discusses Milton Friedman's warning when the Fed is asked to engage in policy that oversteps its role.

We have had recently had a spirited discussion on monetary policy during the "secondary depression" by Steve Horwitz and George Selgin.  I agree with the logic of the position of Steve and George (and Hayek).  But I wonder if under our current set of monetary policy institutions, and the critique that George (and Steve) have made of those institutions in the past that they are capable in practice of pursuing the "secondary depression" policy that Steve and George (and Hayek) are advocating.  What if, due to the "long and variable lag" in monetary policy, the effort to stabilize MV results not in stabilizing MV, but results instead in inflation.  Is the Fed engaging in the odd practice of being a driver who upon discovering they just ran over a pedestrian with their car so they decide to back up over the body in the attempt to undo the damage?

In a world where our monetary policy institutions are imperfect, aren't we asking too much of them to handle the "secondary depression" smoothly?

Could this ultimately be the reason why F. A. Hayek argued beyond a monetary rule and instead for the denationalization of money?  Milton Friedman moved from trusting the policy makers in control of acting on the monetary rule, to advocating that monetary policy be entrusted to a computer.

Again, I understand and agree with the logic of the argument that George and Steve (and Hayek ... and Yeager) are making.  But I wonder about its effective operation in the world under the existing set of monetary policy institutions.  And I would argue (as I believe both of them would agree) that under a free banking regime, the market forces at work would have "automatic stabilizers" that would accomplish through normal market adjustments by banks the monetary "rule" that is impossible to implement in a central banking regime.  So isn't it a mistake to insist that a central banking system engage in monetary policy that would mimic what the market forces would predictably accomplish under free banking?

I am way out on the limb here because monetary theory and policy is not my field of study, so my questions may be very innocent and wrong-headed, and I usually defer to George and Steve (and Larry and Roger) when questions of a macro/money are raised.  But something doesn't seem right to me about entrusting the Fed to manage monetary policy to ease the "secondary depression" when it was Fed errors that contributed to the "depression" in the first place.  We have information and interest-group reasons to suggest that this institutional regime simply cannot do what we are asking it to do.