It's not quite so simple as that, right? The single currency was never billed as something that required individual countries to give up their autonomy to centralized EU institutions. If it had been sold as a package deal from the start, the Euro never would have happened to begin with.

The lesson Europe seems to have failed to take from the US is that federalism is a Trojan horse. The U.S. federal government was billed as being sort of like what the EU government is pitched as today, but ultimately destroyed the sovereignty of the States and reduced them to administrative divisions that have to take orders not just from Congress, but unelected bureaucrats at random federal regulatory agencies. And it wasn't some slippery slope process, but necessity. States in a federal union have none of the tools of international relations. California can't embargo imports from Michigan that, e.g. don't meet its environmental standards. It can't threaten economic sanctions against Alabama for its treatment of minorities. It can't bomb anybody. The only way to avoid race to the bottom problems becomes pushing more authority up to the federal government.