The Fed is an independent entity whose mandate is to insure a stable monetary system which means a balanced supply and demand for money as well as control over inflation. They are NOT mandated with preventing recessions or depressions. The Fed Chairman is not a cabinet-level position.
I believe the Fed’s true purpose is to ensure, if not maximize, member bank’s profitability. Looking at greatly increased interest rate differentials between bank deposit rates and their lending rates during Alan Greenspan’s term as Federal Reserve Chairman helped educate me on this point.