And the NCR is explicitly doing an old world speed run and rotting away faster than america did.
And yet it's the faction most favored by Obsidian. To the point where their NCR Veteran Rangers are as powerful as Brotherhood Paladins, despite the lack of energy weapons and power armor.
Best ending in NV is wildcard.
It depends on the Courier. In most cases, however, the Courier just seems to replace House as the tinpot dictator of New Vegas. Now whether it becomes North Korea or Singapore is up to the player's imagination. To be fair, the title "no gods, no masters" is a misnomer for the quest, since you become the Mojave's new master, and if the Courier has a God complex, they can even go full Caligula and declare themselves the new god. Who's going to stop them? The other factions? They don't have a Securitron army with missile launchers and grenades.
The brotherhood would still evolve but I imagine it would still go to something more... feudal no matter what, even with lyons at the head. It would just be more like how a feudal system is ideally supposed to work instead of what it actually ended up in fallout 4.
That was what they were doing in Fallout 3. Trying to take control of the Capital Wasteland from the Super Mutants and raiders, ensuring supplies like water are delivered on time, waging war over resources against rival factions like the Enclave, as well as conscripting locals into their ranks as soldiers, like what any feudal lord would do. They were a feudal state in Fallout 3, but that was too much for the "true Fallout fans", so Bethesda made them dickheads again, because the "true fans" whined that they were too nice in Fallout 3 and wanted the Brotherhood to be dickheads again. Despite, you know, the fact that the FO3 Brotherood is
still a militaristic cult that's seizing power over an entire area, whether or not the locals wanted them there? So they aren't necessarily all peaches and cream. But no, that was still too much change for the "true fans" of Fallout, so things were pulled back in the next two titles.
So the Brotherhood became dickheads again in New Vegas and Fallout 4, because Obsidian and Bethesda got the memo that the Brotherhood ALWAYS have to be reclusive dicks who act like assholes towards everyone. Which kinda explains why I always got the urge to butcher them like pigs, especially since New Vegas was my first Fallout game. When I first heard of them, I wanted to join them to gain access to power armor, but after they put a bomb collar on my Courier and tried to make her their slave
TWICE, (I went to the Sierra Madre before making contact with the Mojave Brotherhood in the bunker) the only thing my Courier wanted to do is to Order 66 the lot of them. She killed not only the paladins, but the knights and the scribes, too. They were animals, and she slaughtered them like animals, because she hated them.
The only time I spared the Brotherhood was to see Veronica's party storyline with them, and to have them be NCR bullet sponges for my NCR playthrough. For every other playthrough, be it for House, Caesar, or myself, I fucking slaughtered them, because that's honestly how my Courier would feel after her nasty experiences with two Brotherhood Elders, and her feelings towards the Brotherhood just get validated by House, Caesar, or Yes Man. Because when an entire faction act like dickheads to the player character, and anyone with a brain in the game's story also hate said faction, it's not that hard to justify genocide against them.
And of course, the Brotherhood wanting to genocide all synths in Fallout 4, even synths loyal to the Brotherhood like Paladin Danse, once again justifies mass slaughter against them. And considering the fact that the Brotherhood started off as deserters from the US army, it wouldn't be that surprising that the Sole Survivor, who is a soldier of the United States, or the wife of a soldier, would slaughter deserting cowards like pigs. Especially when there's more than a few factions that want them dead, including their son's faction. A Sole Survivor who fights for their beloved son and his vision for the future would have no qualms slaughtering the Brotherhood.