I'd say nay. I think it allows maximum freedom for your characters and a nice blank slate for the writers if they just keep setting the new games in different places. With respect, I think you overestimate how connected everything is in this universe. It's not a whole country anymore, and the "governments" that exist aren't really states in the way we understand them today. The NCR is obviously the closest thing to one that we see, but they're all the way out on the West coast and don't have a lot of reason/ability to communicate with the East (though they are expanding). The Legion's territory is large from what we hear, but they aren't really a modern government; just a military dictatorship (that is really close to collapse, one way or the other). It seems to be a collection of tribes that all contribute taxes/soldiers to the Legion, which isn't very sophisticated. They've got some kind of law and a system of slavery but their foreign policy seems to just be one sentence: "Submit or be conquered." If/when they fall it'll affect those within the territory and anyone currently fighting them, but their sphere of influence has only come into play in one game so far.

With that in mind, why would someone from the Commonwealth know or have reason to care that an Enclave contingent in DC failed to poison the water there? Project Purity doesn't supply water to the East coast or even as far as the Commonwealth, it just supplies the Capital Wasteland.

Your 500 hours in Fallout 3 weren't meaningless, they were just meaningless to anyone who doesn't live in the DC metro area (because those are the only people your actions had any effect on). The largest governing body in 3 is the Rivet City Council, and their jurisdiction doesn't even extend into the broken bow of their ship. Beyond that they just distribute water.

The regions of the former U.S. are just loosely organized clusters of communities. Even if you go full Minutemen in 4 you don't make a government, you basically form a militia that agrees to protect a loosely organized group of communities in this one region. It might have the beginnings of one; but it's not a state in the sense of the NCR.

I agree that this direction makes it difficult to make a direct sequel to any of the games, but I don't really want one. I'm ready to see what happened in other parts of the U.S. and tackle new problems/factions/enemies.