They shouldn't and that's exactly why states are allowed to declare bankruptcy and why Puerto Rico should be allowed to declare bankruptcy. States in the EU probably should be able to also.
Greece could default, but it was not clear what would have happened to their central bank, and if a default would have pushed Greece out of the Eurozone.
Due to these uncertainties, and undoubtedly also to pressure from the rest of the EU, Greece decided instead to renegotiate their debt with the Trojka.
Not really. Greece was never allowed to default properly. The referendum George Papandreou alluded to at the time, is a prime example of what I'm saying: Greece defaulting might drive Italian bond prices through the roof at that point the monetary union would be destroyed overnight.
Now that the debt has been turned from public to private, it might be easier to handle as a situation, but I doubt the EU is able to handle such a crisis gracefully.
Greece is stuck to a never-ending extend and pretend program which will effectively kill the Greek economy in the 21st century.
Greece is a sovereign country. It could have defaulted if it really wanted to. Maybe it would have required an exit from the Euro, but that would have been its choice. That they considered this worse than the alternative was also their choice.
I think an orderly bankruptcy process would have been preferable to either of those options. If I was in charge of Greece at the time I would have left the EU over it. I'm amazed Britain left and Greece stayed.
Due to these uncertainties, and undoubtedly also to pressure from the rest of the EU, Greece decided instead to renegotiate their debt with the Trojka.