The euro zone maelstrom refuses to end. Thanks to the debt crisis, some Greek officials are contemplating dumping the common currency for the drachma. Meanwhile, Italy and Spain teeter. A decade after the shared currency was heralded as a 21st-century tool for peace and prosperity, it turns out that currency unions aren’t such a hot idea.

Not so fast, though. This is undeniably a period of epic turmoil, and many economists will tell you that sovereign states need sovereign currencies—full stop. But this notion ignores a fundamental truth: Countries with t...