Greece can't recover because its exports are too expensive. Devaluing the currency in which those exports are sold in order to spur exports doesn't solve the underlying problem, which is Greek productivity. Imagine that the German economy is a Prius and the Greek economy is a truck hauling a ton in a trailer behind it, and the Greek truck is complaining that it costs more in fuel than the German Prius to get from the same point A to the same point B. Devaluing the Greek currency is like making fuel cost less especially for the Greek truck with no change in cost for the German Prius; sure, if the fuel is cheap enough for the Greek truck then maybe the Greek truck will be price-competitive in getting you from A to B, but the real solution is "how do we get the Greek truck to first dump the ton it's hauling behind it and then how do we make it more fuel efficient".
In a single-currency market, it is the responsibility of strong players to shore up the economies of weak players, or risk popular discontent in the weaker economy and the democratic dissolution of the common currency. German politicians have paid lip service to this but have not really put German resources to use in building up the PIGS economies because such a policy is unpopular with the German voting public, which wants to see those resources stay in Germany and to the nearsighted benefit of German taxpayers. This is the real root of the Euro crisis. There were always going to be weaker players in the EU, and it doesn't matter if it's Greece, it could very easily have been some other country. The question is what do stronger players do.
The US doesn't suffer from this issue because, to use an oversimplified example, California voters aren't discontent with FEMA funds used in hurricane disaster recovery areas. Californians are Americans before they're Californians, by and large.
> There were always going to be weaker players in the EU
This is true, however there were quite strict criteria (the Maastricht criteria) put in place to try and prevent this from being too bigger problem. In hindsight, those criteria weren't sufficient, in one way or another.
I believe it's correct to say those weaker economies benefited from adopting the Euro the short term, and that they wanted to join the Euro.
As a twist, the Euro was somewhat unpopular in Germany when it was introduced, because it made things more expensive. So there is a feeling that Germany "paid" the price of adopting the Euro - whether this is true or not is irrelevant for the sake of policy-making.
Even worse: Germany, an already very strong nation, gets to free ride the Euro for its export machine at the cost of its Eurozone rivals (and other competitors in Europe broadly). If Germany had its own currency, it would be considerably more expensive than the Euro is today, which would make German exports more expensive. As you note, countries like Greece, Spain, Italy, Portugal would do better because their exports would be cheaper under less expensive national currencies (unique to their individual economic circumstances), enabling them to compete better against Germany's exports. This artificial prop can be seen in the fact that Germany has the world's largest trade surplus as a percentage of its economic output.
But that is exactly the point right? If you devalue the common currency then the amount you pay Greek farmers goes "up" effectively, and the price you pay German farmers also goes "up" so the relative costs of things stay the same and nothing changes. Whereas with a translation layer (currency exchange) you can "adjust" what it costs Greece and what it costs Germany to the advantage of one or the other.
A tariff is a way to adjust this economic cost externally which takes it out of the market's hands and put it into a political realm and one step removed from the actual economy that should be adjusting.
In a single-currency market, it is the responsibility of strong players to shore up the economies of weak players, or risk popular discontent in the weaker economy and the democratic dissolution of the common currency. German politicians have paid lip service to this but have not really put German resources to use in building up the PIGS economies because such a policy is unpopular with the German voting public, which wants to see those resources stay in Germany and to the nearsighted benefit of German taxpayers. This is the real root of the Euro crisis. There were always going to be weaker players in the EU, and it doesn't matter if it's Greece, it could very easily have been some other country. The question is what do stronger players do.
The US doesn't suffer from this issue because, to use an oversimplified example, California voters aren't discontent with FEMA funds used in hurricane disaster recovery areas. Californians are Americans before they're Californians, by and large.