The Eurozone's Growth and Stability Pact commits Member States to running no more than a 3% GDP budget deficit.

They are forbidden by the U.S. Constitution from imposing import or export duties.

European Union Member States cannot restrict the flow of goods, services, people or capital among themselves, and import or export duties with third-party states are probably harmonized via the EU which negotiates before the WTO on behalf of the Member States.

Capital markets and most large banks are, at minimum, national in scope. They can charter banks that are confined to their states.

The scope of retail banks in the EU is still only a member state (even when a bank owns a subsidiary in a neighbouring state, it operates as a different bank - examples I am familiar with include NatWest operating in Spain and Raiffeisen in the Czech Republic, but I don't know what the situation is between two Eurozone countries). Capital markets are still at most regional. Euronext integrated Paris, Brussels and Amsterdam, and there were talks of a merger between Deusche Börse and the London Stock Excange, but that's about it, other than that the markets cover single member states.

States do not issue currency, though I do not know if they are specifically precluded from doing so. They can issue bonds.

It is unclear to me how the issuing of currency works within the Eurozone, but each Eurozone member state can issue its own bonds. The Member States' central banks still exist and retain a certain set of competences, and only some of the powers have been transferred to the European Central Bank. There is a "European System of Central Banks" which gathers the ECB and all the Eurozone member states' central banks.

It seems to me the Eurozone is almost there if we aren't there already.

When the capital development of a country becomes a by-product of the activities of a casino, the job is likely to be ill-done. — John M. Keynes