During WW1 and WW2, some countries (France and the UK) pooled their resources so they could fight together better.

Then a few years after the war, the European Coal and Steel Community was created to regulate coal and steel in six countries under a single authority. Including West Germany, which had only been formed from the occupied territories a year before. It was certainly not unrelated to military force.

Its initial aims included making war between member states impossible, and eventual democratic unification of all of Europe. The later institutions up to the EU grew out of it.

So although it was completely peaceful, it's still an outcome of WW2.

The original decision by the various states to join together was not at all accomplished by armed conquest.

>The original decision

That's true but blatantly ignores things like, oh, you know the Civil War that tore the US apart

> Membership in it is purely voluntary. This makes it quite unique.

NATO arose from the ashes of conflict but membership is entirely voluntary, and unlike leaving the EU there is no talk of 'punishing' those who no longer wish to remain.

For example France left the NATO integrated military structure in 1996 and rejoined in 2009 without penalty.

To be more precise: in 1966, France left indeed the integrated military structure, but it did not left NATO itself which is also a political structure. The goal of de Gaulle was to have all French troups under only French command (and not US or UK who were leading nearly everything then in NATO) and to have all foreign military bases leave France, so that France regains its full sovereignty. De Gaulle was very critical of the US wars led at the time actually and he wanted to have Europe independent from both the USSR and the USA (and as he considered the UK as the pawn of the USA and not reliable in their commitment to Europe, he was opposed to them entering the EU). A fun fact was that it was also a incidentally a smart move economically, even if those US military bases closings were hurting the towns they were in: because of the Mansfield agreements around precisely 1966, Germany which still had US bases was giving more and more money as part of participating to the defense of Germany (2 billions $ in the year 1971 alone for example). This is quite like what president Trump tried to reinstate very recently by presenting a bill to Angela Merkel, but Germany now is not the same as West Germany in 1966.

You are comparing apples and oranges though. NATO is a purely military alliance. It has no control over the non-military affairs of member states, and little or no effect on the day-to-day lives of member states' citizens. The EU, on the other hand, acts very much like a central government for its members and exerts a lot of pressure on them to make them comply with its policies. That's why I compared it to empires.

What exactly are to "punishments" the EU is giving the UK that you are talking about?