The Greek crisis has given new life to the superficial argument that the eurozone isn’t working because its monetary union hasn’t been accompanied by fiscal and political union.

President François Hollande of France has called for a eurozone government, with its own budget, which would be accountable to the people via a new eurozone parliament. Pier Carlo Padoan, the Italian finance minister, has backed the idea — also advocating a eurozone unemployment plan.

The European Union’s “five presidents” — Jean-Claude Juncker of the European Commission, Mario Draghi of the European Central Bank, Martin Schulz of the European Parliament, Donald Tusk of the European Council and Jeroen Dijsselbloem of the Eurogroup — have given nuanced support for these ideas. In their June report, they called for a eurozone treasury (effectively a finance ministry for the bloc) and a “common macroeconomic stabilization fund” that could help countries weather shocks.

The five presidents first want eurozone countries to converge toward best practice on improving competitiveness. They then want legally binding rules to ensure they stay competitive. They also advocate more coordination of macroeconomic policy between the bloc’s 19 countries, with ultimately some joint decisions on national budgets.

Such an ambitious centralization of economic power is neither needed nor desirable. Nor is it politically achievable.

Creating a common eurozone finance ministry, government, parliament and budget would require a new treaty. This would need the unanimous approval of the 19 countries in the bloc, and probably of the nine other members of the European Union that do not use the euro, like Britain.

Even if many eurozone governments agree that political union is needed, they do not agree on the details. Germany, for example, thinks more fiscal discipline is the main imperative. Wolfgang Schäuble, its finance minister, was reported last week by The Frankfurter Allgemeine Zeitung to want to take away from the commission its current power to police budget rules on the ground that it is too political and soft.

Some other governments, by contrast, think the eurozone has already signed up to too much austerity. Not only is there the original growth and stability pact; there is also the six-pack, the two-pack and the fiscal compact — a bewildering array of budgetary rules that are so constraining in theory that they have often been breached in practice.

But say the governments could agree on what they wanted. Given the sharp rise in euro-skepticism, there is little prospect they could then persuade their people to back them.

If Mr. Hollande called a referendum, Marine Le Pen of the National Front would have a fantastic platform to rail against the loss of French sovereignty. Even the Italians are becoming euro-skeptic: Beppe Grillo, leader of the Five Star Movement, the country’s second most popular party, has called for Italy to abandon the euro, describing it as an “antidemocratic straitjacket.”

Doesn’t this then mean the eurozone is doomed? If 19 countries share the same currency and lose the ability to devalue when they hit problems, surely they also need a common treasury to cushion the blow? And then they need a common government and parliament to give legitimacy to their actions, right?

Not so fast. The crisis of recent years has two main causes: lack of competitiveness and excessive government borrowing. There are better ways to address problems of competitiveness than by agreeing on a treaty to mandate it; and we have already seen that treaties requiring fiscal rectitude have been pretty useless.

To lift competitiveness, the eurozone needs to free up markets. This will also allow the bloc’s economies to adjust more rapidly to shocks rather than millions of people being turfed out of work.

To be fair, the five presidents acknowledge this. Action is needed at a pan-European level to complete the single market in services, the Internet and energy. Creating a capital-markets union would soften the blow when a national economy suffered a downturn by spreading the pain across Europe.

The presidents also rightly call for more efficient national labor and product markets. They want each country to set up an independent competitiveness authority to drive this forward.

While this may be a good idea, the presidents are wrong to suggest that common standards for competitiveness should be hard-wired into laws applying to all 19 countries. This looks like a recipe for rigidity that will hamper innovation.

What about debt? Surely there have to be rules to stop countries from borrowing too much?

Not really. Market forces also provide a possible solution. The key is to allow excessively indebted eurozone states to go broke. Preventing this was the cardinal sin in the Greek crisis.

If investors knew that governments could go bankrupt, they would be more cautious about lending to them in the first place. The discipline of the markets would replace the discipline of the bureaucrats. The German Council of Economic Experts backed this idea in their special report on the Greek crisis last week.

So there are market-based alternatives to political union that could keep the eurozone’s monetary union on the road. They don’t involve a large transfer of sovereignty to Brussels or the imposition of one-size-fits-all policies on 19 diverse countries. As such, they are also preferable.