Well I certainly agree with Ikael's post that there is a problem with the views of the Greek population, who want several things that are incompatible with each other, but if you're a politician it's quite a big call to make. There are economists who'd advocate for exiting the EMU and others who'd advocate for austerity until the end of times, but either way they'd be making a decision that the majority of the public oppose. I agree a referendum isn't an ideal way of managing economic policy, but at least in this situation it forces a choice that the people will have to experience and judge for themselves instead of leaving them in some sort of economic limbo-land or purgatory.
Funny how you say "around the world". It's not a coincidence that the PIIGS nations had sovereign debt crises in the wake of the GFC whilst non EMU nations like UK, USA, Canada, Japan, Australia etc... did not.
The GFC didn't (just) expose flaws in these economies, it exposed the fundamental flaws in the design of the EMU and the ideologies of those who make its decisions. Australia and Ireland both had government surpluses running on the back of high private debt before the crisis: guess which one collapsed and had to be bailed out and which one was able to successfully implement bank guarantees and stimulus through deficit spending? Greece and Japan both had high levels of government debt and persistent deficits prior to the crisis: guess which one collapsed and had austerity enforced on it and which one kept doing its thing and maintaining low yields on its bonds? These aren't 1:1 comparisons, but to act like the economic woes and triumphs of EMU nations are entirely of their own doing and directly comparable to any fully sovereign country is wilful ignorance.
In a world where there was no GFC and Greece stayed using its own currency (or even if only one of those occurred), there is no way it would have collapsed in the way it has now. There would have been no imposed austerity and its troubles would have been its own to sort out over time.
Budget deficits and debt to GDP are compositional indicators, not evidence of a poor economy in and of themselves. Austerity doesn't work. The IMF modelling using a negative fiscal multiplier was proven to be completely wrong. If Greece had more successfully implemented austerity (in terms of increasing tax take and reducing expenditure, i.e. taking money out of the economy) they only would have been more wrong. Other nations reducing their government deficits tells us nothing about what sectoral balances are appropriate for Greece in a macro-accounting sense.
Whatever the problems with Greece's economy are (and I'm not denying there are many) they were only made worse by its involvement in the EMU and the austerity imposed by the Troika. To which you could say " well they shouldn't have joined/been let in in the first place," and I'd agree, but if you think that their admittance to the EMU was an act of benevolence and of no benefit to nations like Germany then you're missing some key parts of the picture.