So, 22 crisis summits on since the eurozone crisis erupted, are the problems now solved? Hardly. France was very keen to push towards much deeper economic integration of the eurozone. Germany, which will end up paying for it, wasn't so sure. What we have ended up with is an agreement to create a single eurozone bank regulator, sometime in the summer.

The problem isn't just that summer may be well too late. Record numbers of Spanish households and businesses have been defaulting on their debts, the Greek government needs more cash to stay afloat, and southern Europeans have been putting their spare cash into bank accounts in the north or property in the UK. Nothing seems to have changed since 22 summits ago.

Being British, I find it hard to be objective about the French, but their idea is actually basically right. A monetary union can only hold together if you have a fiscal union as well. That is, a centralised tax and welfare policy. That is because in a monetary union, states cannot devalue. A country that produces its own currency can respond to economic problems by devaluing – much as happened in the UK during the years after 2007. That makes its good cheaper abroad, boosting exports, and at the same time makes imports costlier, so people economise on them. Eventually, the country starts to recover. But states such as Greece and Spain cannot devalue. When crisis hits them, they really suffer.

The US has a monetary union between its 50 states – they don't all produce their own currency – but it is also a fiscal union. If there is a problem in one state, such as a devastating hurricane, federal funds go out from Washington. That buys the breathing space for the local economy to recover. The eurozone could in theory become such a monetary and fiscal union, and the problems of the Club Med countries could be alleviated – but only by turning the eurozone into an effective superstate, like the US federal union. The trouble is that Americans think they have a lot more in common with other Americans than, say, the Germans think they have in common with the Greeks. So few countries would submit willingly to that central control.

The compromise thrashed out this week is that there will be no all-out fiscal union, but a step towards it – a banking union with a single bank regulator, namely the European Central Bank. The idea is that the ECB can prop up failing banks in the troubled states, and so avert a financial crisis, without anyone going so far as to say tax, welfare and spending policy should be completely centralised.

The argument is that the ECB can exert some discipline on hopeless banks like those in Spain, or cash-starved banks like those in Greece. And maybe a touch of discipline like that would be useful. However, to put all the eurozone's banks in one regulatory basket is asking for trouble. Central banks have not proved themselves to be good regulators. The Federal Reserve, set up to end bank crises and closures, managed to close down the entire US banking system itself in the early 1930s. The Bank of England managed to turn a drama into a crisis by squeezing down on UK banks in 2008, just as they were running out of money – hardly fulfilling its role as 'lender of last resort'. It might well do a better job of regulating banks than the Financial Services Authority, which didn't even see the crisis coming, but it is hardly a shining example.

And this is the snag in the eurozone. A one-size-fits-all banking regulator will not actually fit everyone. And when it does make a mistake, the mistake will be catastrophic because it will affect the entire eurozone, not just a single country. It is asking for real trouble.