Greek banks have aggregated capital & reserves of 45-50 billion EUR. In total, they hold about 80 billion EUR of Greek soverein debt in their portfolios. If those assets need to be written down by half, the capital & reserves of Greek banks will be wiped out.
When banks have wiped out their capital & reserves, the present shareholders have lost everything. That may be hard for them to accept but such is capitalism.
After having written down half of their Greek sovereign debt, Greek banks should be banks in reasonably good condition but without capital & reserves. They would need to replenish the 45-50 billion EUR capital & reserves which they had before the write-downs.
Whoever provides those new 45-50 billion EUR will be the owner of the Greek banking system. Does Greece really want the EFSF to be the owner of the Greek banking system?
Greeks hold deposits in accounts with Greek banks of almost 200 billion EUR. If those Greek depositors could be persuaded to swap 50 billion EUR of their deposits into new capital & reserves of the "cleaned-out" Greek banking sector, they would be the sole owners of the Greek banking sector. And they would be shareholders of banks who should be in reasonably good shape and, as a result, be able to pay more in dividends than they presently pay interest on bank deposits.
Should one not be able to "persuade" Greek depositors to do this, it would be within the realm of Greek legislation to force them to do it.