After reading over these post's, surely a halfway comprimise is the best option.
Have the BoS in fo4, but as with 1 & 2, have the Bos as a non-essential part of the game.
Definately add other/new factions, but you can't say "BoS have been in it too much now, get rid of them."
Otherwise as another poster put it, you would have to get rid of everything that made the transition from isometric to fps because "They've been in too many fallout games now." so a Fallout game with no NCR, Followers, Mutants, Ghouls, Vaults, Brahmin, Enclave, Deathclaws, Dogs, Power armour, Khans, the list goes on and on.
Oh sorry the Radscorps would have to go too, they were in fo3 AND nv after all, so "too many fallout games" again.
It would have to be a vault dweller, nope, been done. A Lone wanderer, [censored] that's been used too. Ummm... I've got it, a Courier. No... wait.
Ok, it would be a pizza delivery boy, who got stiffed out of a payment, had to clean the kitchens as a punishment. But now he roams the wasteland. No wait, too many wastelands by now. He roams the perfect, rolling, grassy plains armed with his sink plunger of justice, (Sink plungers ok? They have been in other games, but not as weapons in or after fo3.) looking to get his caps, ummm.... Those little plastic things they put on your pizza so the lid doesn't get squashed, yeah those things. He's trying to find the guy who ripped him off, so he can get those back.
Oh and as for the "How did they get there from where they started" questions about the BoS. It's been 200 plus years since the war. I know america is big, but I'm fairly sure that people could walk pretty much anywhere in 200 years.
Radscorpion, and others critters are part of the game because it doesnt matter where you go, you find them, they are not factions, they dont need a explanation to appear
BOS on the other hand
We dont need them to make a Fallout, they aren important until Bethesda decided to did it in Fallout 3
Imagine if the NCR or Legion appears in other region that wasnt West Coast???
And for the "walking" thing, thats a poor excuse, what about the danger of the wasteland?, without mentioning that Legion is in east direction, at least of course, they used other way to reach DC,
Or Bethesda Magicka