Greece can't compete within the Eurozone because of the value of the Euro and it can't invest in it's own infrastructure because it has to borrow at 5%+ interest. Germany, for example, borrows at negative interest currently. Eurobonds would mitigate such issues.
Whatever bullshit was going on in Greece at the time when JP Trichet was in office... they ended up passing the buck to the ECB. Instead of telling them to fuck off, declare bankruptcy and start anew in their own currency they mitigated the local fallout with Mario Draghi genius plan (retarded actually) to buy Greek gov't bonds off the SECONDARY market. THIS DID ABSOLUTELY JACK SHIT FOR GREECE. So with 20/20 hindsight we can absolutely state that the first affirmative action by the Eurozone was not intervening, but mitigating the fallout.
Sequentially, when the Troika decided to 'rescue' the Greece/EU, not only did they first bled the EU in order to mitigate the fallout they also forced IMF/EU regulatory oversight. Which is arguably worse because they now borrow at a net. ~12% interest. Part of this is interest, part of it is included in the loan in the form of IMF/EU oversight as part of the monetary support package (this amounts to about 10% of the money borrowed in IMF services).
The analogy is being in a marriage but your partner rapes you every night and you can't afford to get a away. And that is why Yanis Varoufakis had to fuck off as finance minster. Because that Dutch politician Dijsselbloem, who is more politician then anything, does not care about Greece or it's people. So they (the troika) made sure Varoufakis got booted from his position. Because they literally refused to listen to his plea of 'don't rape us'.
If you think "why would they do such a thing?" I refer to the first paragraph: They, like you said, expected Greece to get their shit together in a system where they could not compete. The ECB initially did not intervene.
So here we are. Greece is doing worse then ever. Austerity reform will make things worse. They need to get out.
And this does not even get in to the point where they, like the U.K. will be in a favorable position concerning exports and be able to shore up their internal economy once they get the hell out the EMU.
Could Greece have been innovative and not be in this position when they entered the EU? I think so.
However, current situation has nothing to do with bringing economic stability. Unless we somehow (will never happen) agree on the fact that it is worth to keep this brain-dead vegetable of a country artificially alive. Forever.
They need a fresh start. Everyone knows this. They just can't afford the default (Eurozone et al.)