> Both the current Greek and the current Italian government made promises of leaving the EU
It's quite late for that, since unlike the Brits they also joined the EMU and thus ceded sovereignity to the EU. This is exactly what Margaret Tatcher warned against: a federal Europe by the back door. Also, organizing a referendum on the topic of exiting from the Eurozone is a violation of EU treaties.
https://en.m.wikipedia.org/wiki/Greek_withdrawal_from_the_eu...
Other EU exits could be less disastrous if coordinated. For instance if Greece and Italy would leave at the same time and negotiate together. For this they would first need to form an aliance like the Visegrad group. Regardless, everyone would have to suffer in such an event due to lack of credibility in the EU project, lack of confidence in national currencies and the Euro.
Should that be fixed too ?
For example: https://en.wikipedia.org/wiki/Treaty_establishing_a_Constitu... (see "ratification")
The EU has a long history of ignoring democratic elections. That, to me, does not seem like a good thing at all, and yet it's becoming ever more clear that if you want the EU to exist at all, ignoring elections will be the cost: Both the current Greek and the current Italian government made promises of leaving the EU to get elected. Both have reneged, but of course other parties are springing up with more forceful leave rhetoric. Now French and German extreme-right parties promise to kill the EU if they get elected, and the more mainstream is forced to also take a more anti-EU stance in each country.
If either France or Germany decides to leave, then the EU experiment is over.