You have missed a few items out.
The original post war idea was an economic common market to aid closer ties, whilst leaving a degree of autonomy. When the UK looked to join in the late 60’s, DeGaulle vetoed our joining, as he knew that the UK would not be an easy fit with the cosy French/German axis. We would question things etc.
Maastricht was the key change as this was the change from a common market to the European Union, seeking closer ties, greater powers for EU, stated goal to move to wards a common foreign and security policy, and essentially sowing the seeds for the U S of E. This also brought in free movement of people. Not in itself bad at the time with 13 member states who all had roughly (give or take) a similar economic profile (ie developed and stable).
We move on a few years and we get the Euro proposed and accepted by some of the member states, the UK abstaining. The European Central Bank is founded in Frankfurt and is based on German banking system. The number of EU states gradually rises, with every new entrant being required to accept the Euro as thier currency. The influence and control of the ECB grows with each new entrant. Remember Amschel Rothschilds quote ‘Give me control of a nation’s money and I care not who makes the laws’.
Enlargement of the EU to 28 countries brings in many former eastern block countries into EU control. Free movement however, means the start of mass economic migration within the EU by EU citizens that the UK is legally obliged to allow as we were signatories to the Shengen agreement. The Shengen agreement also makes it easier for non-EU economic migrants to travel through Europe unchecked, as formal borders are non-existent.
In 1939-45 the Nazi’s, ably abetted by the Vichy French, managed to invade and control 11 countries in Europe, and a total of 20 worlwide. The ECB currently has control of the currency of 23! Remember Rothschild’s quote! A certain state has tried to dominate twice by the gun, and failed, but at the moment, it has succeeded financially. (Remember Merkel telling Greece what it could and couldn’t do!)
A close trading zone with peace treaties is to be valued, but the European project has become much more than that, and really only can either fall apart (as all empires do eventually), or become a single entity. The USA became that single entity, but from a starting point where there was no long standing difference in the constituent population, as most Americans are immigrants all with the same ideal of forging a new future. The USSR was formed the other way via ruthless oppression of constituent countries.
The individual countries of Europe though have very different cultures and outlooks, and long histories of alliances and enemies, and whilst it is admirable and desirable to try to seek to avoid future conflicts, it is surely achievable without losing all national identities and debasing cultures, and having to form a U S of E.