That wouldn't make much sense as the BOS and especially the Mojave chapter does not have the numbers to take over the entire region, I think even against New Vegas they would have a hard time, left alone be able to take it over.
I think they could do it if Vegas didn't have a Securitron Army and if they had HELIOS One armed and activated as a weapon. Without House and the Securitrons, what exactly does Vegas have that would pose much of a problem to the BoS? There's no way the Kings, Chairmen, and Omertas could stand against a resurgent Brotherhood. If the NCR and the Legion wear themselves out and withdraw from the region (or are slaughtered and/or nuked by the Courier), I could see the Brotherhood dominating what's left of the Mojave.
They are to much in decline to become a super power again, that is why Father Elijah searched for technological means such as the Big MT and the Sierra Madre to gain an edge over the big wasteland powers without having to go as far as recruiting outsiders into the BOS.
I don't think the Brotherhood is going to attain super power status on the level of the NCR or the Legion (their membership requirements prevent them from growing to that size), but if all other factions were weakened or wiped out I could see the Mojave falling more or less under their control by default. I imagine a largely empty desert, with Brotherhood patrols (accompanied by the army of Eyebots they created from ED-E) picking over the ruins, extorting food and supplies from the remaining communities and roughing up any wasteland savage they caught with advanced tech. Not exactly a pretty picture, but then again, most of the endings aren't great for the average joe either.
I do kind of wish there was a Brotherhood ending option if the player joined up and chose Independence without Securitrons.
Really? The Mojave chapter is easily the most unlikable of them all and abandoning the Securitrons seems kinda counterproductive...
Those judgements are entirely dependent upon what kind of character I'm roleplaying. While I don't like the BoS personally, I do think they are preferable to the Legion, and in some ways, the NCR (!).
But consider it from a roleplaying perspective: for the average wastelander, gaining access to the Brotherhood really would be the equivalent of a medieval dirt-kicking peasant being raised to the rank of knight - and given a full suit of armor, along with a band of knightly brothers who have your back. You can see how that would be an attractive option for the dirt-kicking peasant! At the end of the day, the BoS are just another tribe or gang, which means that they act as an extended surrogate family for their members. This is why people join gangs, after all. If you've never had a proper home or family, suddenly being given one that will protect you (in this case, with power armor and laser rifles and super sledges) is very meaningful. With Elder McNamara in particular there's a real warmth when he welcomes you into the Mojave chapter (i.e. "you'll always have a home here" etc). The desire to belong to something greater than yourself is a powerful force.
Does that mean I think the Brotherhood's ideals would result in a prosperous, fair order in the Mojave? Not at all...but not everyone is motivated by such large scale and idealistic concerns. In fact I'd argue most human beings aren't, and are simply loyal to their tribe
because it's their tribe. That's a big part of the reason why "war never changes". It's perfectly possible (and in fact rather fun) to roleplay a character who supports a paramilitary cult like the BoS out of a sense of tribal affiliation.
As for the Securitrons, I can think of a lot of reasons to abandon them. Yes-Man is hardly the most stable personality, and I don't know if I'd trust leaving him in charge of a network of robotic killing machines. Arguably too if both the Dam and the Securitrons were destroyed, there would be little of interest in the Mojave for great powers, which means that ordinary people could finally go about rebuilding their lives and societies without the threat of being invaded by some empire next door. It could be framed as a sacrifice of power and stability for long-term peace.
More abstractly, the robots represent a particular set of values of the Old World that some find objectionable: there is something to be said for Caesar's claim that at this moment in history "the world needs warriors, not gadgets". I've played couriers who agree with that sentiment but not with the barbaric totalitarianism of the Legion.
Or from the perspective of the BoS, a self-policing system of robots run by a rogue AI is a grave threat to humanity and like all advanced tech,
must be brought under the control of the Brotherhood or destroyed. If that's what you believe, then the choice is pretty clear.
