On the one hand, I'm not well versed in Cold War history. On the other, those examples are valid for actual history; not necessarily for Fallout history. Unfortunately, I haven't found sources leading to either direction. At the very least, Korea was more probably not divided; otherwise the Chinese would have invaded south Korea either along with or shortly after Alaska (not doing so leads to a hostile country far too close for comfort that military depends on your currently enemy). On the same note, I wonder why China didn't invade Japan.
The interventionist (and somewhat questionable) policies of USA IRL during Cold War are a moot point: We're talking about a universe that runs on 50's "science" and was unable to create more efficient engines. I'm guessing that any policy that allows USA the be the only superpower in the world is fair game, but I fail to see how (for instance) helping the European countries would do that. Yes, you gain a potentially powerful ally against URSS, but you are also feeding a potential rival superpower (As Europe was for a good part of history).
GRANTED: The 13 commonwealths were created to "strengthen" the internal structure of USA (note that it was counterproductive) to stand against communism. That doesn't necessarily mean international alliances. Real life USA didn't (probably cause wasn't seen as necessarily, or sane), but they did associate themselves with other powers.
According to what I can collect from the fallout wiki, the union of Europe was quicker that what you give it credit. For instance, the
Treaty of Rome was 16 years early, the "Western European Union" established a pan-European army based in the
Treaty of Brussels (hard to say since when, but somewhere between 1948 and 1996). Having a unified army means that the European commonwealth can't be "loose affiliation of nations" (not more than the constituent states of RL USA). In fact, I consider that this could only be possible if the general public see the USSR as a bigger threat than IRL (one way is not having USA helping them) or the guy making the time-line not caring.
If NATO did exist, then it was inoperative by the Resource War. Why? Simple: there is no mention to outside help to or against USA during it. Also, there are no references to USA help in the European war (not even "in spirit", for instance formal declaration of war).
From a gameplay perspective, it makes more sense. However, China should probably have it's own alliance (to avoid the IA making peace and reflect the virtual Chinese's control of southeast Asia and other portions). Besides, USA plus all of Europe against Middle east would be overkill (and leave USA open for a Chinese attack)