Thing is, it's inconsistent with the level of destruction you can see in the game. Just compare buildings leveled to the ground in Boneyard and pretty much intact ones in Capital Wasteland.
Not necessarily, there are plenty of buildings which are shown to be standing considerably high. In the original Fallout you can see some very high buildings remain throughout Necropolis and huge skyscraqers are seen still standing pretty high in the intro movie of Fallout: Tactics.
I know, I know, you'll probably say that Fallout: Tactics is non-canon or something to that effect. Nonetheless Necropolis has huge buildings which can be seen both in Fallout's intro movie and in Necropolis' load map screen. I'm sure the same can be said of other cities, even perhaps in Washington DC where anti-missile defense systems might have deflected too many direct hits. I checked out some pictures of Hiroshima and I can see structures similar to the Capital Wasteland still standing in some areas.
Still the statement was more regarding the fact why the Eastern Seaboard is less developed than the West. Even if Washington didn't sustain many true direct hits, the concentration of radiation might have killed everyone in that area while perhaps other Eastern areas where hit much more directly.
I think the explanation that the people in the Capital Wasteland having migrated in from other areas such as mid-eastern states is reasonable enough to explain the lack of civilized progress storywise. Naturally the practical, non-ingame, reason that the Capital Wasteland is less advanced is because Beth wanted the game to reflect the look closer to the original Fallout which was more desolate than Fallout 2 where progress had developed for just around a century.
In any case back on topic, I think there may be a possibility to at least hear about previous protagonists both in New Vegas and Fallout 4. Of course in F4 it depends where exactly the game will take place, given that communication across vast distances should still be fairly limited. The best one could hope for would be to hear about the LW or CO from a traveller who was there during those events or if radio stations such as GNR manage to extend their signals with repaired towers.