The Brotherhood is basically finished. Even if the NCR loses the Mojave - and that is often the outcome when I play New Vegas - there is no guarantee that the Mojave Chapter survives. Literally every faction wants them destroyed; even Yes Man would prefer you take them out. In my opinion, it would be a strange Courier indeed who would allow the BoS to live and also be opposed to NCR (or Legion) hegemony.
Even if they do manage to survive, I doubt they have the vision or the initiative to take control; they will likely dwindle into irrelevance, or be destroyed by whoever does win Vegas. In the ending slides, all they can think to do is to take control of the highway and shake people down for energy weapons; that means they have become little more than raiders, no better than Vipers with power armor. That shows a distinct lack of imagination and vision, and ultimately that will spell doom for them in the long term.
I mentioned before that I wish there was an option to ally with the Brotherhood as a primary faction in New Vegas, with them marching into the Strip and reclaiming all the shiny bits. But this would require you to completely destroy every other faction, and short of Lonesome Road's nuclear option becoming canon, I just don't see the BoS playing a major role again on the West Coast.
Frankly, the best option for the Brotherhood is to have the Courier negotiate a peace settlement with the NCR. In the short term, this guarantees their immediate survival. In the long term, it forces them to acknowledge and interact with the outside world. In other words, you break their policy of isolation and force them to accept the reality of the post-nuclear world, instead of hiding away in a fantasy world (in this sense, the BoS are basically a bunch of basement dwelling losers, who rather than growing up and getting involved in the world, would rather stay underground and just LARP as knight errants of the realm. No wonder they are always the heroes of the Bethesda titles in the franchise...).
I'd like to think that in the event of an NCR victory, the Brotherhood becomes incorporated into the Republic as an experimental division of the military, focused on research and development and special ops - kind of like the "good" ending for the Brotherhood at the end of Fallout 1. Out of all the possible developments for the BoS, this one was always the most attractive for me and I think it's unfortunate that they devolved into such a fanatical organization.
Usually though I wind up blowing up their bunker. I tend to agree with House that the organization has outlived its usefulness, and represents a threat to any attempt at rebuilding civilization with anything approaching a pre-war level of technology.
Assuming that NCR expand in the same manner as it is, I can agree, BoS is on the lose side and will definitely fail. The thing is, I can't see it that way. Every single faction as we know got their pros ans cons, for example, the reason why the Vault City did not expand was they limited source of power, which was the Vault generator. We already know that New California Republic is in bad shape, because:
- Upcoming food crisis,
- Long years of war with Brotherhood of Steel, and later with the Legion,
- Economic crisis leaded by the BoS assault on the gold reserves (which forced the NCR to set the currency on the water once again),
- Thousands of casualties (even more wounded in the battle and disabled later on),
- And the final, most fatal thing - the cost of managing operations in the Mojave desert,
Those are not trivial things, this are greatest problem that Republic will need to face, tougher than fighting with the Legion, BoS and all California riders at once. From my perspective, power of the NCR is rather snowball effect, achieved from uniting the wastelands communities. It's definitely prove that rebuilding civilization is possible. I also got the filling, that NCR forget about their foundations. We can see that the interest of the "big and wealthy" is above the interests of the communities that are within the NCR. That is even greater problem -
the civil unrest.
Don't get me wrong, maybe I look like the hater, but I really like the New California Republic, I enjoy playing Fallout 2 and Fallout: New Vegas while siding with them. The thing is that I just can't see the NCR in their current form. It would be also interesting to see civil war in the California, leaded by for example Vault City or the Hub (i assume that San Francisco is nuked down by the Enclave as a part of the Van Buren).
The last thing that I think off, is that after the event of the Fallout: New Vegas, New California Republic is in the desperate need of peace. Here I would rather assume (if the Brotherhood hepled down in the battle of Hoover Dam), some kind of ceasefire treatyis possible. Both sides are weaken, leading to rise of criminals and group of raiders in California.