Britain's vote to exit the European Union has done Europe an enormous favor, no matter whether you think "Europe" is a good or bad idea.

If you think it's a bad idea, then Britain is about to prove that it is possible to leave and survive. The transition is going to be expensive — Britain will enter a recession in the short term, and the long-term transition may be even more painful than the short, particularly if London cannot retain its position as the financial capital of Europe. But if Britain wants to be a country rather than a city-state, it's a transition it will have to make at some point. Merely by proving it can be done, Britain will give heart to any other state reconsidering rule from Brussels.

But if you think Europe is a good idea, then you must think it can be made to work. And the only way Europe can work is by becoming a deeper union. The euro can only function if Europe has a common fiscal policy. Europe can only wield diplomatic clout commensurate with its demographic and economic bulk if it has a common defense policy. And Britain was always going to remain the largest, strongest foot-dragger to further cessions of national sovereignty.

Now, given America’s failed experiment with the Articles of Confederation, and the painful experience of the American Civil War, you would think we would appreciate the need for unity, and an effective central government. But in fact, we strongly opposed a British exit precisely because of their foot-dragging.

The United States only ever wanted Britain to remain in the EU because we always favored a broader Europe over a deeper one. We wanted to make sure a country that saw the world in similar terms to the way we saw it remained inside the European tent. And we opposed a more deeply united Europe that might steer its own course apart from America, particularly if it developed a genuinely independent defense capability outside of NATO.

It has never been obvious that this policy has been in America's best interest rightly understood. If Europe is to be our ally, then we need that ally to be able to pull its weight. A weak, dysfunctional, and dependent Europe serves nobody's interests, including America's. Those who really believe in a functional version of a European Union, as opposed to a fantasy version, must believe that Europe can become, over time, something more like a nation. And if that is what Europe is to be, then an ever-broader union is a mistake, inasmuch as it makes deepening the union ever more difficult and expensive. If Europe must deepen, it must first shrink.

"Deepen" does not necessarily mean becoming a highly centralized, unitary state, much less a homogeneous culture. The United States' federal system reserves considerable power to the several states; Canada's federal system reserves even more power to its provinces, as does Germany to its Länder and Switzerland to its cantons. There's no reason why Europe could not go down a similar path.

To do so, however, its founding members must compromise their conflicting visions of what Europe is supposed to be. Germany is going to have to accept that it has an open-ended responsibility for the welfare of citizens of other European states. Not for the states themselves, much less their leaders — but for their citizens: Germans will have to come to see Greeks as more like Ossis than like Ausländer. And France is going to have to accept that a functional Europe is one in which France is just a large and powerful province rather than an empire of its own.

That price may not be worth paying, for either country. If it isn't, Britain's impending exit gives these two central states to the European project the opportunity to rethink, and renegotiate, the project itself. A less-ambitious, confederal Europe that stuck to being a common market might well endure better than the current arrangement — and might entice Britain back in.

Meanwhile, if Europeans decide to pay the price for true union, and the gamble pays off, then some in Britain may come to regret having missed out on the opportunity to be present at the creation — or, alternatively, to have prevented it. But Britons should abjure regret. This is not the 19th century. Britain cannot decide the fate of the continent. Nor can it be central to its affairs. In the context of a united Europe, Britain can either be an independent nation and bridge between Europe and America or it can be an important but ultimately peripheral province of a united European state.

By leaving, the British make it possible for Europe to choose its own destiny, and for Britain to choose whether and how to join it.