But they are connected. The Vault Dweller left his Vault, and stopped the Master from taking over California. The Chosen One, the grandchild of the Vault Dweller, destroyed the Enclave's Oil Rig sending them retreating East, to DC. Where, the Lone Wanderer fought them and destroyed them finally, with the help of the DC Brotherhood of Steel chapter that was sent east two decades earlier. Back west again, the Courier decides the fate of New Vegas, and finds a robot, ED-E, that has travelled all the way from Adams AFB in Maryland. Then, in Fallout 4 the Sole Survivor battles Kellogg a man from the NCR, and the DC Brotherhood of Steel show up.
So a game that is set in the whole of the former United States?
I think a game set in the Midwestern United States... say Chicago, could make for a great area in which to tie ins to all the past game.
Chicago would have the Midwestern Brotherhood of Steel. Possible remnants from the Enclave. It's not far from Springfield Illinois where Abraham Lincoln is buried. So I can easily see Hannibal Hamlin and his Temple of the Union there and a way to get one one of the best weapons in Fallout 3, Lincoln's Repeater. I can see the MWBoS making the Chicago are somewhat stable area and a center for trade. If the MWBoS are still in Colorado and New Vegas might suggest that they are. Then that would would be a means of having information from the events of New Vegas working it's way back to Chicago. Even information from all the way back in the NCR itself. Traders talking about California, the Legion and a city of Sin protected by robots in the middle of a desert.
With the events of Fallout 4, depending on future DLC. We know Arthur has become a dictatorish like figure. After the Institute is destroyed his next target could be the MWBoS itself. Thus tying in the events of Fallout 4.
So to sum it up. We would know of what could have happened in DC since Fallout 3, what happens to Boston after Fallout 4, the long awaited information since the end of Tactics and of course what happened since New Vegas.
How about an https://www.youtube.com/watch?v=7P5T0hedTX4?