The Greek banking system is and must be a ward and contingent liability of the state. At this point in the tragedy, the banks should be nationalized and probably merged. There is no real point in multiple banks if they are all going to be state-owned for the next decade. The more banks there are, the more potential bailouts and self-dealing by management.
The financial system and the sovereign are one, whether people like it or not. The idea of somehow separating the banks from the state and having them default in their own private ways is spectacularly ill-advised. Depositor protection must come before government bondholders and the troika. Deposits are sacred liabilities of the nation; they are not "investments", and depositors are not "investors".
Greece cannot repeat the Cyprus mistake of defaulting on or confiscating bank deposits. All other liabilities (including pensions and Target2 balances) must be subordinated to bank depositors. This is because bank deposits are the money supply, and without money an economy can't operate. MxV = PxT. As M declines, so will both P and T.