Can't we go back to the BOS in Fallout 1? The proud, strong and big faction that actually influenced the wasteland?
That faction is gone, it has been explained in Fallout 2 why they went into decline. (not accepting new members because of xenophobia, the idea that they possessed the most advanced technology which they felt the outside world could not handle responsibly, the secret wish of waiting out until everyone else died off so that they would inherit the world.
Even in Fallout 1 the organization was already suffering because of its politics and interpretation of the Codex. They had not recruited outsiders for decades and made a recruitment test that kills almost everyone who is willing to go through with it in order to deter people.
In the best ending they became a house of development that slowly reintroduced the advanced technologies they hoarded. Perhaps they did for a while before they went back into self imposed isolation.
These days the West Coast BOS and the NCR are even at war because the West Coast BOS feels that they should be the sole possessors of advanced technology, forcing people at gun point to turn over power generation tech, computers, and energy weapons.
The Mojave Chapter only survives because they realize that they will just get more enemies if they go out and holding up people to search them for possession of inappropriate technology.
McNamara the most progressive member of the Chapter is not willing to do much necessary changes because he knows the rest of the BOS would not accept these.
Eventually the West Coast Brotherhood will die out, and it is their own fault.
The only way the BOS would come back is if someone completely ignores Fallout 2 and Fallout New Vegas.