To those of a glass-half-full disposition, Europe’s prospects haven’t looked this promising in years. The recovery is gathering pace, helped by an improving global outlook, low interest rates, a weak euro and the end of austerity. Surveys show manufacturing activity and economic sentiment at their highest levels since 2011. Unemployment is falling everywhere: In Germany at 4.1%, it is the lowest since reunification; Spain has just recorded its sharpest increase in jobs since 2008. In Italy, where real household disposable income is rising at its fastest pace since 2001, an overdue cleanup of the banking system is under way, addressing one of the biggest risks to the European economy.

Of course, this good economic news is overshadowed by political risks. After the events of 2016, including the surprise election of Donald Trump and the Brexit vote, few are willing to bet against further revolts against the established political and economic order. Looming elections in the Netherlands, France, Germany and possibly Italy will provide further opportunities for voters in major Western democracies to register their disillusionment with globalization in general and the European Union in particular by handing power to anti-EU populist parties.

But at the risk of slipping into 2016-style complacency, these anxieties look overdone. Two months before the Dutch elections, the Party for Freedom, or PVV, led by Geert Wilders may be ahead in the polls, but it remains far short of a majority and is likely to be shunned as a coalition partner by other parties. A French poll last week showed far-right National Front leader Marine Le Pen trailing the conservative François Fillon ahead of May’s presidential election. Under certain scenarios the poll also suggested Ms. Le Pen could be beaten to the second-round runoff by the independent centrist Emmanuel Macron. In Germany, polls show Angela Merkel’s Christian Democrats still lead all other parties in support by a wide margin, including the anti-immigrant, euroskeptic Alternative for Germany.

The prospects of a populist breakthrough are perhaps greatest in Italy if there is a snap election this year, with the 5 Star Movement currently neck-and-neck with the incumbent Democratic Party. Even so, the hurdles to a referendum on EU membership are formidably high.

Indeed, one lesson of 2016 is that economies and markets have developed a high degree of resilience to political risks. The Brexit vote has barely dented the U.K. economy, buoyed by booming consumer spending despite a near 20% depreciation that has reduced real incomes. Similarly, Mr. Trump’s election has reinforced growing market confidence of a pickup in growth and inflation. Households, businesses and investors appear to have concluded that elections change nothing; It is what governments do that matters. Besides, Europeans have plenty of experience in incorporating populist parties into mainstream coalitions, as is currently the case in Finland and Denmark. Even Geert Wilders’s PVV was part of a formal parliamentary pact from 2010-2012.

Arguably, the real political risks for Europe stem less from elections than the EU’s persistent governance crisis. That is evident in a marked deterioration in the Continent’s ability to find common solutions to common challenges, leaving it increasingly vulnerable to shocks. In the early stages of the eurozone debt crisis, the EU was able—belatedly and under extreme pressure—to improvise bold solutions, including the creation of common sovereign bailout funds and a banking union.

But over the past year, the EU has struggled to take decisive political action in the face of multiple challenges as its complex decision-making processes have become increasingly unworkable: Plans to resettle refugees remain in limbo, Greece’s bailout risks being derailed by political differences among its creditors. Meanwhile, a trade deal with Canada was nearly derailed by the parliament of Wallonia, and an accord with Ukraine was halted by a referendum in the Netherlands.

A vicious feedback loop has developed. The EU’s struggle to find common solutions to common problems has undermined its credibility and legitimacy in the eyes of voters, fueling support for antiestablishment parties. In the eyes of many, the EU is now seen as an agent of insecurity rather than security.

At the same time, rising support for populist parties is worsening the governance crisis at the national level, making it harder for governments to deliver the overhauls needed to tackle the scars left by the financial crisis in the form of high debt burdens, unaffordable welfare systems and low productivity. In a highly integrated EU economy—and particularly within the monetary union, which lacks common shock absorbers—national problems can quickly become common problems, bringing instability to the whole continent and highlighting the EU’s own governance deficiencies.

None of this may matter if the economy continues to recover and the EU is spared the need to make further tough political decisions. But the list of challenges confronting the EU in 2017 is daunting: It needs to negotiate deals on Brexit, Greece and strengthening the EU’s border protection and asylum systems to maintain confidence in the Schengen border-free travel zone. The bloc also has to complete its banking union, and to put in place further shock absorbers to ensure financial stability when the European Central Bank ends its government-bond buying program. And that is before whatever unknown unknowns that 2017 may bring.