That, and exactly that is the problem. And you know what? Germany is trapped in this system just like all other countries as well. The effective income in Germany stagnated after the introduction of the euro while it went up nearly everywhere else.
This is true. But this was a German political choice. Haartz IV. They held down wages to boost exports. In a fixed currency system there's a name for this. It's called Mercantilism. And it's against Eurozone rules. By suppressing wages, the Germans boosted the competitiveness of their exports, while also restricting domestic demand within Germany. The downside of this is that capital builds up in German banks, but there's nowhere to spend it, as demand is low.
The banks had to pay interest on those savings. So they had to lend it to someone. There was insufficient appetite for borrowing in Germany, so the German banks recycled this money across the Eurosystem as loans to Spain, Greece, Italy etc.
But now Germany would like its money back. Understandably. But those countries can't pay Germany back, because Germany won't buy their goods, because Germany likes to run huge trade surpluses. The Eurozone solution to this has been to cause deep recessions in Southern Europe, thus massively pushing up unemployment and forcing wages down. This has destroyed internal demand, so now the Eurozone has a large trade surplus with the rest of the world - and those trade surpluses can be used to pay back debts within the Eurosystem.
Of course this causes deflation all across the world, as the Eurozone and China both push policies to repress internal demand and boost exports. The better policy would be a bit of inflation to help reckless debtors a bit and punish reckless lenders (but only a bit) - and allow wages in Germany to rise faster than those in the Eurozone periphery. Also structural reforms to make their economies more competitive. Although breaking up the Euro in an orderly manner would be the best policy choice of all.
If the Germans had stuck to the Eurozone rules, they wouldn't have done this internal devaluation. They also wouldn't have broken the Growth and Stability Pact in 2003 (without penalties). And they'd have been taking action to reduce their trade surplus once it topped 6% of GDP 6 years ago (also in breach of Eurozone rules). Now who was it who called the Eurozone "a rules based organisation"? Ah yes, it was Merkel. Repeatedly. And Schaeuble too. Repeatedly. And rather smugly. And I suggest, incredibly hypocritically.
This is one reason why Italy entered the Euro with a trade surplus with Germany, and now has a deficit.
Also it's causing the increase of inequality in Germany. As workers aren't getting the benefits of the export boom, it all goes to profit.
Separate currencies are great for dealing with this problem. Making people take wage cuts is difficult and painful. Wages tend to be sticky. It takes unemployment to push them down. But a currency devaluation does this to everyone for imports, but doesn't effect internal trade so much. So can cushion the effect.
Oh, one more thing - if you want to see what happens to a developed nation that overuses QE, look to Japan.
It's too early to tell. Japan's problem was allowing deflation to take hold in the early 90s. Their economy has stagnated ever since. This is what the Eurozone and ECB were allowing, until they finally announced QE this year.
Although they have allowed deflation to take hold in Italy, Spain and (most disastrously) Greece. And QE was designed to exclude Greece, who need it most.
Whether Abenomics will work, who knows. But Japan now has both growth and inflation, for the first time in 20 years. If they can get the economy to keep growing, then their debt is sustainable. If not, it won't be. Rather like Italy's. If the Eurozone can't meet its own targets, and give Italy 2% inflation a year, along with some growth, then Italian government debt will have to be written-down. Given that all the major Italian opposition parties are now calling for a Euro referendum, they may solve their problem by leaving. Unless the Eurozone start pursuing policies that work for everyone, not just the core.