I think it's not all black and white, and there's actually a bit of both at play. Eurozone Countries now have no choice but to achieve increased levels of fiscal and political coordination. That process will inevitably produce friction, but this would have happened even without the currency. If anything, a heightened level of friction creates an urgency that would not otherwise be there.

If you are looking at it from a Brexit perspective, consider that shedding skeptic countries that never joined the Euro is a good thing in a federalist sense, since it makes it easier to achieve consensus in a smaller and more committed group.

In a way, losing Greece or Italy would have proven Friedman right, but the opposite happened: the Euro survived, Greece and Italy now are forced to drive their economy from a European perspective. De-facto political unity is happening, country by country.