The Maxon child was sent out the to D.C because, get this; "The Brotherhood's High Elders decided that he would be safer in the Citadel under the protection of Elder Lyons than anywhere else in the wasteland"
Even in FO1, there was a certain degree of Factionalism within the Brotherhood.
In FO3, we see that this sort of thing can cause outright divisions and splits - the Outcasts leave Lyons' Brotherhood, to continue their mission as THEY see it.
...
It is thus not beyond plausibility that had young Maxson remained in the West, he would have been the object of a political tug-of-war, as each of several factions within the brotherhood sought to control and influence him. That sort of power-struggle, with a young boy at the center, could not be but devastatingly harmful to the boy in question.
Not to mention the possibility that his presence, and the resulting struggle for control and influence, might have been even more dangerous
to the brotherhood itself.
Thus, one solution to both dangers: get teh boy out of the West - put him at arms' length somewhere where he'll still be educated as a Brotherhood Squire, where he'll still learn his heritage ... but where not only will the internal power-struggle politics of the Brotherhood not affect him,
he won't affect them, either. ...
Very much a "King Arthur" sort of story, and I wouldn't be surprised to see FO4 or FO5 explore young Maxson's return to power. Possibly aided by a wastelander standing in the role of Lancelot ... and controlled by
us, as the protagonist of the story. Whether that return will be in the West, or based out of the revitalised D.C. ruins in the East, who can say?
I can even see the idea of the Brotherhood's mission changing (under so much influence from Elder Lyons, and his daughter - on whom the boy is explicitly stated to have a crush), to one of
rebuilding; conserving the tech of Yesterday not solely for the sake OF conserving it ... but to see that it is leveraged to bring as much prosperity and peace as possible to
Today.
With that vision in mind - and with access to top-secret files on computes in D.C. (and in the Vault-Tech headquarters); if time jumps ten or fifteen years ahead, a lot of those collapsed building sections around D.C. could have been excavated - the new Brotherhood might start seeking out Vaults and opening them
now, to recruit more educated, civilised people
who have a familiarity with technology into their ranks. Hopefully by peaceful means, unlike the Enclave, of course!
The protagonist of a future game could be just such a person. Ultra-tech (like power armor) might be in short supply, but being given a choice right off between, say, a 10mm pistol or a Laser Pistol, as well as getting a suit of leather armor and handful of assorted chems, would be suitable IMO. Then, you get sent out on a mission to X or Y new area, to aid in the initial "explore, stabilise, assist, and recruit" process ...
That could actually prove workable as a game premise, at least as a a START of one.