Your analogy is flawed because prescribing antibiotics is routine and known to all doctors. The 1930s Fed was in uncharted territory and they didn’t have our benefit of hindsight.
No flaw at all. The Fed was created to intervene in financial crises the largest banks had handled at times prior to the Fed. A decision to not do something is an act of decision making.
And the Fed did intervene in the financial markets in the early part of the GD by raising the discount rate and by selling gov't bonds. One explanation for that is that maybe the thought they were defending the gold standard, which does not readily allow for an expansion of the money supply.
The Fed always has been and always will be an institution where its decisions to act, or not act, will have influence on the financial markets and the economy. People wait with baited breath to discern whether today's Fed will act to bring about increased interest rates, or not.