The deeper cause of the crisis, however, is that the C.S.U., which has dominated Bavarian politics for decades, is threatened by the growing popularity of Alternative for Germany, or AfD, the bigoted nativist party that is now the country’s third largest. That’s in part because the C.D.U. has dragged its Bavarian sister too far to the left, creating an opportunity for the AfD among traditional conservative voters.

But mostly it’s because Merkel created the conditions that gave the enemies of the European ideal their opening. She refused to cap the number of asylum seekers Germany would take and then pleaded with other European countries to take them. That almost certainly gave Brexiteers the political imagery they needed to carry the vote a year later. The AfD was a minor Euroskeptic party before the refugee crisis gave it a rallying cry. The xenophobes of Austria’s Freedom Party, Italy’s Northern League and Sweden’s Democrats have all profited politically from Merkel’s decision.

Generosity is a virtue, but unlimited generosity is a fast route to bankruptcy. Humanitarianism is commendable, but not when you’re demanding that others share the burdens and expense. A very liberal immigration policy is wise, but helter-skelter migration isn’t. Knowing how to set broad but clear limits is one of the essentials of conservative governance. Merkel’s failure is that she ceased to be conservative.

Admirers still speak of Merkel as if she is Europe’s last lion, the only leader with the vision and capacity to save the E.U. There is much that is admirable about the chancellor, but as things now stand she is likelier to be remembered as the E.U.’s unwitting destroyer. The longer she’s in office, the more the forces of reaction will gain strength. And isn’t 13 years in office more than enough?

There is still time for the E.U. to be saved. Europe needs a real security policy, backed by credible military power and less dependence on Russian energy. It needs to regulate migration strictly outside its borders so that it can remain open within them. It needs robust economic growth and much lower rates of unemployment, not paeans to the virtues of sustainability and work-life balance. And it needs institutions in Brussels that aren’t mere regulatory busybodies trying to punish member states for being economically competitive.

What’s the alternative? A passage from Norman Davies’s magisterial history of Europe suggests the darker possibilities:

“Inter-war politics were dominated by the recurrent spectacle of democracies falling prey to dictatorship.” He continued: “It cannot be attributed to any simple cause, save the inability of Western Powers to defend the regimes which they had inspired. The dictators came in all shapes and sizes — communists, fascists, radicals and reactionaries, left-wing authoritarians (like Pilsudski), right-wing militarists (like Franco), monarchs, anti-monarchists, even a cleric like Father Tiso in Slovakia. The only thing they shared was the conviction that Western democracy was not for them.”

The stakes are too high for a muddler like Merkel to stick around.