The Federal Reserve Board acts as a lender of last resort and a general control of the money supply. Something that is absolutely necessary in a modern economy. While each bank that is part of the federal reserve does technically own shares in the Fed, the government has the whip hand.

The dramatic booms and busts of the 1870's-1900's were in large part due to the lack of a central bank... and most of the ones up until the Great Depression was because the Fed was often reluctant to do anything.