Of course Greece could have exited the Euro and partly defaulted on its debt. The disadvantages are that the new Drachma would be a very weak currency such that the remaining debt (in Euro) would be fairly high in Drachma.
But in the long run well-functioning European institutions which prevent such issues, namely a central bank committed to IMMEDIATELY being a lender of last resort, a fiscal order which creates rules that guarantee long-run low levels of public debt while allowing for deficit spending in the short run plus last but not least the ending of trade imbalances in Europe (which basically implies that Germany raises its wages), are preferable in my eyes.
Once again, I am not reading everything which the IMF publishes but it is definitely unfair to portray it as a neoliberal economic institution. We all read our Stiglitz (if not, Globalization and its Discontents is a must-have-read), it surely was one during the last decades. But it made a turn 2-3 years ago towards not defending austerity anymore.
The problem isn't the IMF, it is in Europe Germany, the European Commission and the ECB. There is of course ample of bad economics out there (mainly on the right but also on the left; while I cherish quite some of Marx's ideas all of his economics ideas are plain wrong) but if you take a look at what fairly centrist economists like Blanchard, chief economist of the IMF or De Grauwe are writing about the crisis you will realize that good mainstream economics isn't the problem but the solution to the sovereign debt crisis.