Emmanuel Macron has put eurozone integration firmly on the political agenda. The new French president may have stopped short of repeating his campaign calls for a euro-area budget and treasury when he met German Chancellor Angela Merkel in Berlin on Monday, his first full day in the job, but the two leaders did agree that action is needed to strengthen the eurozone—and that this could even involve changing the European Union treaties. The challenge now for eurozone governments is to agree on what exactly has gone wrong and what they should do about it.

The biggest problem with the euro is that it hasn’t delivered the economic convergence voters expected when it was launched; in fact, it has led to divergence. In 1999, living standards in Germany, France and Italy measured by gross domestic product per capita were broadly the same. Today Germany is significantly richer than France, while Italy has seen its GDP per capita slump from 119% of the EU average in 1999 to below 90% today. Spain’s gap in living standards behind Germany has remained almost unchanged since 1999, but Portugal and above all Greece have seen their relative positions decline, Simon Tilford of the Centre for European Reform noted in a recent report.

Flaws in the original construction of the euro are clearly to blame for much of this divergence. The single currency was supposed to make it easier for countries to finance themselves by removing the risks associated with volatile exchange rates and illiquid bond markets.

At first, this worked as intended, with the euro’s launch triggering large flows of capital into financially stressed eurozone countries as interest rates there converged with those of Germany. But when the global financial crisis struck, euro membership turned out to offer little protection against sudden stops in funding after all: In the absence of a lender of last resort, many economies struggled to refinance the excessive debts they had accumulated in the boom, leading to a credit crunch and deep recessions.

These defects were addressed by the creation of the European Stability Mechanism—the eurozone’s bailout fund—and by the launch of the European Central Bank’s quantitative easing program in 2015. Those measures gave the eurozone its lender of last resort and drove down borrowing costs in crisis countries, paving the way for what is becoming an increasingly robust recovery.

But those changes haven’t proved sufficient for driving the eurozone toward renewed economic convergence. Although some former crisis countries—notably Spain and Ireland—have now been enjoying strong growth and falling unemployment for several years, growth in Portugal and Italy remains weak, while Greece’s recovery appears to have stalled amid new tensions over its bailout.

Such disparities are a reminder that not all the problems in the euro area can be blamed on flaws in the single currency. What has determined the pace of recovery has been the speed with which countries have been able to reallocate resources—both human and financial—to more productive uses. Spain and Ireland exited quickly from the crisis because unlike Italy and Portugal they took decisive action to clean up their banking systems, allowing credit to flow again to viable firms. Spain also overhauled its labor market, leading to a much faster pace of job creation than in less-flexible France. In much of southern Europe, inefficient judicial systems and weak insolvency regimes frustrate efforts to tackle bad debts and deter new investment.

This is the context in which proposals to deepen eurozone integration should be judged. Sure, the creation of a common euro-area budget could help soften the impact of future shocks by helping to relieve pressure on domestic budgets, creating the fiscal space for other adjustments needed to help economies rebalance. But it provides no guarantee that member states will make those adjustments. Indeed, the availability of fiscal transfers could create new moral hazards, reducing the incentive for countries to make reforms that might improve long-term economic convergence. After all, Italy has been a currency union underpinned by generous transfers for over 150 years, yet this hasn’t prevented the ever-growing divergence between its North and South.

Besides, it is doubtful whether the eurozone could create a common fiscal capacity with the firepower to play more than a modest stabilizing role in a crisis. Member states may be reluctant to increase contributions to the EU when they already face having to make up the shortfall arising from the U.K.’s departure. Nor is it clear they would be willing to accept transferring enough sovereignty over sensitive areas such as labor-market and welfare policies to underpin proposed initiatives such a common unemployment insurance fund.

In any case, the importance of a common budget shouldn’t be overestimated. Studies show that even in the U.S., transfers from the federal budget help cushion only 13% of the impact of regional shocks to output; it is private capital markets—equities and credit—that absorb two-thirds of such shocks.

Policies designed to boost cross-border investment flows—including extending the EU single market, completing its banking union and deepening its capital-markets union—may not match Mr. Macron’s ambition for eye-catching political theater. But it is on such unglamorous work that the fate of the eurozone ultimately hinges.