Omigod, how can you both be in the EU and yet so ignorant about the nature of the sovereign state to which your leaders now pledge loyalty? The EU is a political union with the power to demand and dictate policy to its member states. It can pass laws that have immediate binding effect throughout the union and issues other laws that are literally directives to member states requiring them to implement specific legislation at the national level. Now it even has official legal personality so it can sign agreements and treaties as its own entity. Even on foreign policy the constitution requires all member states to adhere to EU decisions and not engage in independent foreign policy. The individual member states are independent countries in declaration only at this point. All are member of a federal republic called the European Union. It is just that no one is recognizing this legal reality at present.
Continuing to think of my crazy North America and Western Europe Federation:
We'd include the rest of the Balkans, Iceland, Norway, and Switzerland.
Turkey... yes, actually, yes, as long as they resumed their secularism, and decreased corruption and authoritarianism.
Next, we'd make of NATO and the new Federation, one and only. NATO would just be the armed forces of the Federation.
What to do about Australia, New Zealand, South Korea, Taiwan, the Philippines, and Japan?
Well, the new nation wouldn't necessarily have the same old treaties held by the US with Japan, South Korea, the Philippines, and Taiwan (since the United States would cease to exist), and there would be no Commonwealth (since the UK would cease to exist).
Then, we'd see. Maybe we'd encourage these countries to create their own super-nation, and we'd engage in close cooperation and treaties with them (Malaysia, Singapore would be their members too; maybe Thailand after regime change; as a matter of fact, all current ASEAN nations, plus Papua-New Guinea, and all the micro-island states).
Similarly, we'd encourage nations like Mexico, Chile, Colombia, Costa Rica, and Panama to form their own super-nation, and would also be very cooperative with them. Eventually they'd join our Federation.
The rest of the world would reorganize too.
Brazil, Argentina, Uruguay, Paraguay, Bolivia, Peru, Ecuador, and Venezuela would merge, together with the rest of Central America.
The Arab World would merge, with the exception of Syria and Iran. These would join Russia, which would absorb Ukraine, Belarus, Moldova, and the Stans with the exception of Pakistan and Afghanistan which would probably join the Arab Bloc. Sorry, Georgia. You'd have to be gobbled by Russia too.
What to do of Israel?
I believe Israel's only hope for survival would be relocation. They just can't survive where they are. They are only standing because of a technology gap (nukes, advanced military) but once the Arab Bloc developed the same technologies, and if the new North American and European Federation did not renew any alliance with Israel, it would be doomed. I don't think the new Federation would be able to afford Israel's defense, so, they'd have to relocate - hopefully, into the new Federation.
So, South Africa and the rest of Sub-Saharan Africa would join China. I'm not sure what to do of India. Maybe they'd stay independent.
OK, so, here is my new world. Let's see how many countries:
1. The United States of North America and Western Europe, plus Chile, Colombia, Costa Rica, and Panama.
2. The South and Central American Federation (with the exception of the parts above that would belong to the USNAWE.
3. The Chinese-African Federation (would also take North Korea, after the fall of the current dynasty.
4. The Arab-Pakistani-Afghan Federation
5. The Federation of Southeast Asia, Japan, Australia, and New Zealand
6. The Russian-Stan Federation
7. India
OK, that's it. 7, instead of the current 196.
It would be a rather stable world.
The stability would come from the "too big to fail" concept. The dilution of nationalism would also help.
These blocs would be so huge that it would be impractical for them to engage in wars. They'd rather have to engage in trade and diplomacy. There would be no more Arab-Israeli conflict.
All right, 100 years of peace and prosperity.
Then the military would become obsolete as there would be no more wars. More mergers would occur between these big blocs. Eventually Earth would be one (by which point space colonization would have started).
I think the path to enduring peace is the progressive extinction of nations.
Too crazy, what I'm saying?
Yeah, probably. Call it Political Fiction (similar to Science Fiction). Probably impossible. But a nice dream.