To be honest I think Fallout should be kept to the US. However if other countries want to develop their own post-apocolyptic game franchises, more power to them. I look at the "S.T.A.L.K.E.R." series and "Metro 2033" as examples of post-apocolyptic games set in other countries.
Strictly speaking, while everyone wants to see some kind of life continue in THEIR homeland when looking at a grim situation like this, it doesn't work. The bottom line to Fallout was that there was a nuclear war and pretty much everyone died. The US is pretty much unique in how "well" it fared being a super power, I've heard some speculation that a bit of it was based on estimates of US defensive technologies Vs. Nuclear strikes, meaning large portions of the US were unscathed to an extent while the rest of the world pretty much got blanketed in death and radiation. It's also noteworthy that one strategic advantage the US has always had from the rest of the world is relative isolation. Meaning that enviromental affects would more easily decimate the rest of the world, especially if that was where most of the successful nuclear strikes were, where sheer distance would protect the US. Of course a lot ALSO depends on the types of nukes used on both sides.
The raw amount of death is what makes it so grim. Right now the only real connection to another nation was in "Tenpenny Tower" and it implies that there is less in England than in the US given that the guy was so impressed over finding a surviving Skyscrayper. Of course I've also wondered if Tenpenny is supposed to be lying about his origins to put on airs.
What's more, too much surviving civilization would mean that the US wouldn't be as isolated as it is. Groups like "The Enclave" would have had contact with survivors elsewhere in the world given their remaining technology, and things would have played out a LOT differantly. If a lot of little settlements survived globally you'd see things having developed sort of like Robert Adam's "Horseclans" by this point I'd imagine.
On top of all of this I myself have mentioned that I tend to think when it comes to apocolyptic fiction, globalization tends to ruin it due to one upsmanship games. The most notable example to me was back in the day when a company called FASA had a fairly successful RPG/Novel series called "Shadowrun" (it's still around to some extent). Due to popular demand they began to expand things to the rest of the world, and it proved to be a huge mistake. There was a lot of bickering and one upsmanship in the writing, and you had outcries over how a guy from Germany developing part of Europe decided that France was pretty much leveled and got it written into the canon. This lead (as I remember) to a French writer doing nasty things to what was undeveloped in Germany. I seem to remember there being a big deal made over some of the ghost writing in the "Berlin Sourcebook" which while quite amusing, turned the city into what was basically a giant apocolyptic asylum, with a LOT what appeared to be German bashing including a bit on "The Berlin Opera" turning into homicidal performance art.
As odd as it sounds, an America-centric point of view tends to wind up being fairly neutral (which is why I believe the setting pretty much went back to the US, and a bit in Asia due to the Japanacorps and such). For all the bashing of US arrogance by others and acting like we're the center of the world, it seems to me that when given the abillity to insert themselves into a world setting like this even the more "mature" areas of the globe start engaging in school yard behavior, and it gradually drags everything down.