In short, those who promoted common currency hoped it would eventually lead to common political institutions. Euro-area members, however, kept their respective seats at IMF, G7, and other international organizations. So the members of the Euro did not completely unify themselves politically. Economic policies do not have to be identical to be part of a currency union but counties do have to put more thought into unintended consequences of their economic policies.
European countries should have put more thought into whether or not joining the Euro was a good idea economically. The United Kingdom ran stress tests to determine whether or not it should join monetary union. Clearly the decision was political and the tests where just a way of checking a box, but more countries should have adopted an approach similar to that of the UK.
France ran it larges current account surplus in its history when entering the Euro in 1999, while Germany ran a large deficit. Twelve years down the road and Germany was running a surplus while France was running a deficit. Why?
It took time for Germany to get back on its feet after reunification. East and West Germany formed a monetary, economic and social union. West Germany was economically competitive and East Germany was not. People in the East wanted to buy goods in the West. Infrastructure and capital stock had to be replaced. Germany chose to reinvent itself by removing parts of its economy which it knew it did not have a comparative advantage. It focused on thinks like technology that required a highly skilled labor force. People began exporting parts and importing partial goods as firms began to embrace globalization. This eventually resulted in destabilizing factors.
Germany saved during the first decade of the Euro which caused problems. As a result of saving, demand in countries in the north decreased will demand in south kept increasing. Before long, countries in the north were financing countries in the south.
The other destabilizing factor was the interest rate policy. The monetary policy had to be set for the euro area as a whole, not individual countries. This means that a country like Germany who deserved a low interest rates was causing other countries like Greece to get the same low rate. In other words, the monetary policy was too expansionary for the countries in the south.