Sorry, by Eurozone, I mean "countries that use the Euro" - not the EU. The EU is largely about trading standards and economic mobility with a bit of social redistribution thrown in, or maybe it's an evil superstate that wants to ban British kettles - one of the two.
In a democracy the leader of a country should carry the will of their people (another topic on which we frequently disagree - but hear me out).
Concentrating on the person of Merkel isn't helpful, we should ask about the German/Spanish/French/Italian/etc people and their principles.
Consider the UK.
If a factory closes in Newcastle then the taxes from people in the south can help soften the blow through benefits or by spending on northern infrastructure.
People in Newcastle can move further south for employment and know they'll speak the language, they'll have similar working habits, etc.
The people of the south and north both see themselves as British. They probably think of themselves as British before Geordie or Cockney (especially as many people in those areas may have moved in from elsewhere).
If the economy is looking dodgy in the north then people don't rush to move their money from northern banks to southern ones.
This social and political uniformity means it obviously makes sense for the north and south to share a currency (
optimum currency area).
But we saw in the last financial crisis that the German people
do have mixed feelings about difficulties in other nations.
Greece/Germany is quite different to the Newcastle/London situation.
Maybe one day people in the Eurozone will see themselves as European first and German/French/Italian second.
I think that'd be kind of nice - in a one-world, hippy sort of way. Anyway - back to reality.
Germany is the exporting powerhouse of Europe. Productive, educated workers making things the world wants to buy.
But in the past they ended up with peseta, lira and other currencies they didn't know what to do with. There's only so much olive oil a German needs.
So they sell those currencies, but who wants them? The price of the peseta goes down. Order is restored.
After the Euro the Germans get paid in (from their point of view) a proper currency. A currency they can pay Germans with.
So the currency flows into Germany, and flows, and flows... (Happy Hans)... until... what?
The Greeks decide to move to Germany and build BMWs? The Germans don't want that (it's not clear the Greeks want it either).
The Germans throw money into Greece to pay Greek benefits bills? Nein! Yell the Germans - have a bridge, a youth sports stadium, or something else cheap and shut up.
I think either a financial crisis will turn the Euro into a failed currency (although it might live in parallel with re-introduced national currencies), the other nations will learn tricks from the Germans (but they'd better do it fast), or we'll see greater social/political union of the Eurozone.
But I don't think the Germans would sing Ode to Joy if they get stuck with the bill of bailing out other counties.
So instead of the Euro being the stabilising antidote to nationalism you desire it becomes a point of contention - a flashpoint.
Of course, all the problems go away if we just do away with currencies altogether as PJ suggested. Don't they?