First error of fact is that the Eurozone wanted a single currency without a government, and modeled his argument after states within the United States. In fact, the eurocrats did want a closer government integration: it was proposed twice, once as a constitution and once as a treaty, with Ireland, of all places, voting it down.
The second error of fact is the nature of single currency zones. Single currency zones have existed, with stability, for long periods of time, without transfers. The mechanism is personal, rather than financial, mobility. The US deliberately, as in it is part of the design of the modern state, pays people to stay relatively put, rather than pour into cities.
This is not to say that Europe's wealthy nations should have let Greece into the Euro, or that once it was in, they should have allowed it to borrow as much as it did – which was against the fiscal terms of the treaty, and well within the ECBs ability to restrain.
The reality is that Greece, like other dollar board countries, had an inflow of capital. Argentina imploded, but then left. This was a heterodox solution that rested on keeping as much of the money in the country as possible a.k.a. currency controls.
Another did quite well: China. China only went off a dollar peg recently. Hong Kong is on a dollar peg, and does well without transfers of wealth.
The problem is that Greece did not discipline its own economy under hot money, and then once that fell apart, Europe prevented the Greeks from doing what was obviously correct: slamming the door shut on capital flight, and negotiating an orderly exit from the Euro to the Drachma. That is to say, what Iceland did.
The Euro was not fatally flawed, instead, it is the people who have run it that were fatally flawed. The 2000's had a profligate US funding two wars. Europe took advantage by exporting consumer goods, particularly to the US, which was also spending far too much on health care and housing. Europe was artificially more competitive, because the US was engaging in protectionism by funding internal economic activity, rather than export activity.
The reality is that Greece is only partially to blame, in that while it is a drug addict, the banks of Europe were more than happy to pump up their bonds portfolios with sovereign loans that acted to a great extent the way mortgages here did: with the back door promise that they would not default. Thus it was not a few mortgages in Maine that unraveled the world banking system, nor is it Spain, or Greece, or Italy, that threatens to unravel the Eurozone. What is happening is a series of speculative attacks on Germany by way of peripheral countries, each attack designed to get the Germans to pour money into a bail in, one that profits bond holders of weak bonds. It has not been a risk free proposition: many of these attacks have left the bond holders sharply short. But over all, it has been a profitable exercise.
The lesson here is for both large and small nations. For small nations, do not allow hot money, and when it starts to flee, slam the door shut. Greece did not do this, and is now caught. Had the billions that fled Greece been nailed down, Greece could make payments and hold out for a better deal, or default and continue to import necessary resources. For large countries the lesson is also simple: do not use small peripheral nations as saps. Hong Kong does not allow it, and Argentina and Iceland have learned, painfully, not to do it.
The US once made the mistake, before a currency union, of allowing one part to wallow in hot money, this was a proximate cause of the Civil War, a recession in no small part caused by Southern excess fell hardest on the North, driving a wedge of hot economic pain to add to the calculus of interest.
Is there a solution for Greece? Now, no. The Greeks have voted for their youth to flee the country, leaving a husk of a nation of pensioners who will vote to pile on debt to keep their checks flowing, for as long as it lasts. Before? Yes.
But that was then, now, Greece will have to perpetually threaten to blow up the Euro to get crumbs enough to survive. The instability of the government is the only card they have: fall, and the Euro falls with them.