Hm, you do realize the Legion brooks no allies, right? Everyone is either ''incorporated'' or killed. That much is pretty clear in game. Big C also ''claims eminent domain'' on all the Wasteland, in fact that's pretty much the entire point of the Legion in the first place.
As for NCR, how ruthless they are depends on the situation. The Khans have been their enemies for more than a century, and opened fire on the first caravans coming to the Mojave, they're a very special case. BoS started the hostilities in their war by basically demanding NCR hand them all their more advanced tech and then destroyed their economy, so the antagonism is pretty understandable, also they're kinda dicks all the time. And you can still broker an alliance, which you cannot with House or the Legion. As for the Enclave, as far as anyone knows they were crazies in power armor who tried to wipe out all life, I'd also hesitate to take chances about them. Do notice that there's nothing in the ending sliders that says they pursued the Remnants, while Lanius does. The Fiends get no quarters for very obvious reasons.
Against more minor enemies/outsiders, they seem pretty accomodating by Fallout standards. Freeside is left alone unless the Kings attacked them. Throwing out the Followers if they don't help is a dick move, I'll grant you that, but they also leave the Boomers alone. Let's remember that, for the NCR to have survived in a universe as harsh as Fallout, they cannot be goody two-shoes. If something poses a real threat, often you destroy it or it destroys you. There's no room here for ''oh, if we just beat them a little and then leave them alone, I'm sure everything will be fine'' nonsense.
Also, using the Divide as an argument seems silly to me. It was a very specific piece of technology that blew up a very specific area (also known as plot device). It's not like NCR runs around detonating nukes for shit and giggles. They make very good use of their tech generally (see all the improvements made to New Vegas while House was sitting on his bum building casinos and making tribals into mobsters).