To many American Europhiles, it seems obvious that furthering European integration and unity — "the European Project," as they say — and finding a deal between Greece and its European partners are identical.

But things look rather different to Europeans. What I've learned over the years speaking to politicians and public officials in Brussels, Frankfurt, Berlin, Strasbourg, and Washington is that many European integrationists take a hard line on Greece in part because they think Europe would be stronger without Greece.

It's a risky approach. Sufficiently risky that few people articulate it publicly. And nobody wants to actively kick Greece out of the European Union. But plenty of people think that Europe should set a very high bar for Greece, and that if Greece responds to that bar by choosing Grexit the rest of the continent will be better off. Here's why.

1) Greece cheated

American economists commenting on the situation don't like to dwell on this point because, macroeconomically speaking, it's irrelevant. But the fact of the matter is that Greece got into the eurozone by cheating. To get in, it needed a budget deficit of less than 3 percent of GDP. Officials presented cooked books in 2000 portraying their real deficit as below 1 percent, even though they've basically never gotten below 3.

Having gotten in by cheating, Greece managed to avoid sanctions for breaking the EU's fiscal rules by cheating some more — this time with the connivance of Goldman Sachs.

From the standpoint of the current Greek government and much of the global left, this simply goes to show how absurd the volume of moralistic outrage directed at Greek profligacy is. Everyone's hands were dirty in this, from giant investment banks to the European Commission's political overseers. Nor was Greece alone in these kinds of shenanigans. France and Germany both found themselves poised to be penalized for violating deficit rules in the mid-aughts, and rather than cheat they used their clout to water down the rule.

But naturally enough, the view of the French and German governments and EU staff is that they are all blameless. The problem with Greece cheating, according to people who are not Greek, is that Greece cheated.

The European Union is, naturally, driven by norms as well as rules. And the overwhelming consensus in European officialdom is that the Greek state repeatedly violated the relevant norms in a unique and disturbing way. The political integration of Europe is inherently a political project, and in political terms the fact that Greece got in by cheating is very relevant.

2) Banking union is happening

Part of the eurozone's problem has been the absence of a continent-wide deposit insurance system. In America, if a ton of banks in Florida fail due to unwise lending in the face of a housing bubble, a nationwide agency — the FDIC — bails out the depositors. By contrast, in Europe, the problems of Irish banks fell exclusively on Irish taxpayers, and of Greek banks on Greek taxpayers.

Europe is trying to fix this. But it would be easier to fix if Greece left the eurozone.

In September 2012, the European Commission — the EU's executive arm — issued a white paper called "A Roadmap to a Banking Union," and over the past two and a half years Europe has been walking down that path. There's even an explainer on how it is supposed to work, though as is often the case with EU documents it reads a bit like a Dutch guy and a Slovenian guy sat down to write an English-language document whose intended readers are Italian. In fact, that's probably exactly what happened.

They key points, however, are actually pretty simple:

The European Central Bank now operates as a eurozone-wide bank regulator, complete with a eurozone-wide set of regulations.

There is a eurozone-wide equivalent of America's FDIC called the Single Resolution Board to ensure bank deposits and handle the disposition of failed banks.

The SRB will obtain the funds it needs through eurozone-wide taxation of banks that operate in the eurozone.

The SRB has even been given a German chair, Elke König, formerly of Germany's bank regulatory agency, so everyone knows it's serious. If you are having a very dull day, you can watch her and her fellow board members be interviewed by the SRB's communications chief in English here:

This is all good news for the long term. But for the medium term, it means that so long as Greece is in the eurozone, the problems of Greek banks are, to an extent, everyone's problems. If Greece leaves, the shiny new system can start working without being burdened by Greek issues.

3) The eurozone's newest members don't like Greece

When the Greek debt crisis really became acute in 2010, the eurozone had 16 members. Today it has 19. The three new members — Estonia, Latvia, and Lithuania — joined after the structural failings of the project became clear. These countries are incredibly enthusiastic Europhiles (they see membership as an implicit guarantee of independence from Russia), and they really hate Greece.

Latvian FinMin has no sympathy for #Greece : "Our economy contracted by 20%, we cut the administration by 30%, including wages and staffs" — AnneSylvaineChassany (@ChassNews) July 7, 2015

Slovakia (which joined in 2009) and Slovenia (which joined in 2008) have also been noticeably unsympathetic to the Greek position. These countries are poorer than Greece, and they feel the idea that Greece deserves special financial assistance because it borrowed a lot of money in the past is ridiculous.

European policymakers, naturally, are enthusiastic about countries that are enthusiastic about the European project. They see the thrifty, eager Balts as the future of Europe and profligate Greeks as the past.

4) If Greece left the eurozone, the eurozone could stop talking about Greece

Europe is a big place, and there are a lot of interesting policy issues that European policymakers could be talking about. There is Russian aggression against its neighbors, for example. There's demographic stagnation in Germany. There's youth unemployment in France. There's what to do about Swiss tax havens. There's trying to form a trans-Atlantic free trade zone with the United States.

But it's hard to focus on anything other than Greece as long as Greece's old debts are perpetually throwing the continent's financial arrangements into turmoil.

It's clear that if an agreement is reached, whatever the Greek government agrees to will be agreed to reluctantly. Once the moment of peril is past, it will likely try to backslide (see above: Greece cheated) until a new crisis arrives. So if Greece stays in the eurozone, it means the eurozone will keep having to focus on Greece. Getting rid of Greece means the eurozone can move on.

5) Europe's emerging fiscal union needs an example

Over the past few years, the European Union has set up a number of measures designed to prevent a recurrence of the 2010 debt crisis.

The way it is supposed to work is that a country that's hit by bad economic times and finds itself in a problematic debt situation can get financial assistance from a general European stabilization fund. In exchange, it has to agree to various budget control measures. More importantly, a country that is using the stabilization fund is eligible to benefit from a European Central Bank program called Outright Monetary Transactions (OMT) that in theory will cap borrowing costs.

All of this — but especially the Outright Monetary Transactions — is regarded with considerable suspicion in Germany and some other countries. They worry the program will become a pretext for the central bank to write blank checks to profligate governments.

The Greece situation, legally speaking, doesn't actually relate to these arrangements. But it does involve the same institutions. If Greece doesn't reach a deal with its creditors, which in turn leads the ECB to demolish Greece's banking system, which then leads Greece to quit the eurozone, that will be powerful proof that Europe is not afraid to punish malefactors — and the example of Greece will make it that much less likely that other eurozone members will let themselves fall into Greece's position in the future.

Vox Video