This is being treated as purely a financial issue. As Marc Chandler has noted however, it is anything but. Greece is an important NATO member and actually has spent its expected share of GDP on defense, unlike most of the other EU states. Some part of the Greek debt stems from that, although I am not so naive not to think that those defense purchases pumped up a lot of insiders' Swiss bank accounts.
A greek exit from the EU might well be followed by an exit from NATO and the establishment of Russian or Chinese naval bases there. Given the current western paranoia about Russia, one would think that would send shivers up the spines of western leaders. Avoiding it would seem to be well worth the relativley small cost of accommodating Greece's debt.
The letter from the new Greek leader in the OP made a certain amount of sense. Greece is insolvent in the accounting sense. It's unclear how extending bad loans and providing new money to pay the old debt advances matters. This idea that sovereign euro debt can never be defaulted on is bizarre. Would the US monetary system collapse if a state defaulted on bonds? Plenty of countries, from Russia to most of South America, have defaulted before and life continued. Why is Greece so special?