Why? When the FDIC steps in, the bank doesn't get to go on operating like nothing happened. They're shut down, the owners of the bank lose their money, and management is fired. It's the depositors who are bailed out.
The entire financial system is built on trust and stability. When a bank is rescued its shareholders suffer (by selling at a loss, nationalization, whatever). It’s not a positive outcome for them, but rescuing a bank has big implications for systematic stability.
