Most of what economists call the 'money supply' is not physical greenbacks. Most of the 'money supply' is what is called 'outside money' - loans, derivatives, and bonds. This virtual money is created by modern banking.
This is crucial to understand. The money supply doesn't exist in the form of dollars, it exists as credit extended from the banking system. Bank loans expand the money supply via fractional reserve banking. The money supply expands whenever loans are made. The size of the money supply is roughly proportional to the amount of credit issued in the economy.
That's how the Federal Reserve controls the money supply. They raise interest rates and it becomes more costly to borrow money, so less people borrow, credit contracts, and the money supply shrinks. They lower rates and more people borrow, credit expands, and the money supply expands.
Thus monetary policy in the US depends upon the existence of a functioning banking system. So what happens if all of the major banks in the US disappear? It's far worse than just the loss of the bank businesses themselves (lost jobs, lost deposits, and so forth). The real problem is that the nation loses control of the money supply. Without banks to issue credit, credit disappears, deflation sets in, and you have yourself another great depression. No thanks, personally.
This is what I was alluding to earlier when I said the banking system plays a vital roll in national monetary policy. The economy depends upon money, and the banking industry is what makes money work in our country. The banking industry is far more important than the car industry.