The historical evidence shows that Austerity causes demand contraction and often demand spiral, it has never in global history solved a budget crisis.
That's like claiming emergency rooms are responsible for vehicular deaths just because so many people die there. No one goes through a crash bout of austerity because they're doing well just as no one goes to an emergency room unless they have substantial problems.
The Euro eliminated currency barriers to unequal trade relationships which substantially hurt the Greece economy.
In other words, Greece fucked around for a couple of decades rather than deal with the above problem. Now they're paying the consequences.
The time to implement austerity and similar measures would have been two decades ago. It's not like the "unequal trade relationship" showed up yesterday.
And austerity does work. The Scandinavian countries successfully practice austerity right now. When you control spending over generations rather than only when your creditors force you to, you can have a much better society.
Debts on a national level will only rise as long as there is demand for that debt and confidence in it, or banks out to make money by selling people shit and betting against it.
It's worth noting here that Greece lied about its financial health for a time (and may still be lying, not like I care). So some of that debt was picked up under false pretenses.