The EU has the Eurozone as an internal block, but not the whole EU belongs to the Eurozone. The economic demise of Europe will pull the Eurozone closely together at a rapid pace, while the non-Euro countries are left behind. Europe moves at a different speed, a different pace. It looks in two differenct directions.
By necessity, the Euro countries need to aim for closer cooperation on a financial/fiscal level. The non-Euro countries, on the other hand, have no direct reason to increase the power of the European Union. There is no incentive for them, and no indication of interest.
Who is in the Eurozone?
The Eurozone consists of; Netherlands, Germany, Belgium, Luxembourg, France, Spain, Portugal, Greece, Italy, Latvia, Lithuania, Estonia, Finland, Slovenia, Austria, Slovakia, Ireland, Cyprus, and Malta. The non-Euro members of the European Union are : Poland, Hungary, Romania, Czechia, Sweden, Denmark, Croatia, and Bulgaria. (Now that the United Kingdom has left.)
Will They Join?
Although some of those are expected to join the Euro in the future as part of them joining the European Union, enthusiasm is limited. It is clear by now how the Euro negatively impacted southern Europe, and how dependent it has made them. There is no real reason why Hungary or Sweden should give up their own currencies.
Perhaps it will change after Soros starts messing with currencies again. He can do so by making them volatile for a profit and destroying the economy as a side-effect. But so far nothing of the sort is happening. His breaking the Bank of England may have been a one-off that was only enabled due to the circumstances at the time. The last twenty years have not given an indicator that small currencies are easily manipulated or malfunctioning.
Not only will these countries not be eager to join the Euro, they will also not be enthusiastic about closer integration within the European Union. Frankly, for most of eastern Europe the European Union is about gaining protection from Russian interference, and hand-outs.
The problem here is that the United Kingdom was able to block such integration up to the moment of Brexit. They were a big powerful player in the EU, comparable to Germany or France. None of the non-Euro countries left are ‘big players’. It puts them at a disadvantage compared to the eurocountries when it comes to discussing the course the European Union needs to take.
This, one can predict, will bring about future strife and complications. Poland and Hungary are already frustrated with the European Union. Meanwhile, Sweden and Denmark are more or less neutral bystanders that observe everything the European Union does with some scepsis.
Ultimately, it is unlikely that any country wishes to join a currency as fragile and broken as the Euro. This difference will likely tear the European Union apart. Over time, tensions between these two blocks will increase. Those that go for a Federal Europe, versus those that wish sovereignty remains with the individual memberstates.
In the United States, a similar question of sovereignty and who had the power was only solved after a civil war. We can hope that the same thing will not happen in Europe.