Well if they want to continue the franchise chronically, as in continue further down the future-line (eg. 250 yrs since the War), they seriously need to rework their portray of the post-apocalyptic world. I'm sure most will agree that Fallout 3, while presented itself rather impressively, feels as if it takes place 200 days since the War, not 200 years.
The major themes of a 200+ year Post-Apocalypse should be the "Return of Mother Nature" and "The Distant Memories of the Past". Most of the civilisation will exist in the form akin to Junktown and Megaton, and most denizens unfamiliar with the term "Ame-ri-ka", while vegetations overwhelm the pre-War cities and towns to the point they are barely recognizable. As an explorer in Fallout 4, it shouldn't even be initially clear that the game takes place in America (unless you read the packaging), as most NPCs of the Wasteland will only talk about the Pre-War knowledge as some sort of myth and stories passed down from their ancestors (picture a mother telling some children a "fairytale on the Great Fires"). Not suggesting everyone should be a tribal, but without a central government and national education, I doubt generations born 200 years after the War in a town like Megaton will care much for American History or even the American identity, when their lives revolve around making ends meet and avoiding raiders and mutants.
A glimpse into a nuked China will be great too - too bad most people don't like subtitles.
You know, I think I'd rather see something very close to the war, say 30 years. Close enough that survivors are desperate, far enough removed that most people who die from the war, radiation, plague, etc are gone. The wasteland would consist of little pockets of people trying to live on what they grow, and maybe the occasional government handout, from a shattered government structure that in many places, have gone native. Still folks around who remember the war, with laments and stories to tell...folks who may know things and would be willing to trade the information for food or booze. It's dark, dangerous, and desperate. There are THINGS in the woods, and no one dares walk the countryside at night. Strongmen are starting to appear, and they promise wonderful things. The military still show up on occasion, although they don't often leave their heavily fortified based. Who knows how much food the hoard.
There is very limited food, but even so, guns start appearing with greater frequency. The young people are moving in bands, fighting like pack wolves. The old get weaker.
Have the choice of being born in the wasteland or in a vault, with each providing a overall trait.