But there's also no indication that there is a end to hostilities between the NCR or BoS either, the BoS did take a heavy beating as a result of the war and retreated into even more seclusion. The Battle of Helios One is a example that both sides still take arms against each other.
But the NCR didn't cakewalk it, the BoS initially had the upper hand but as you mentioned with the Van Graff quote; "My family has enough men and weapons to field a small army, but the NCR can field a really really big army."
We only know that the Mojave Chapter took a beating and went underground. They stayed there due to leadership issues. IMO losing that battle and losing Elijah shocked the chapter, paralyzing them.
Lore says the brotherhood have a state within NCR. NCR was forced to change from gold coins to money because of the Brotherhood war. BoS were hitting the gold shipments so people were not getting paid. If all the brotherhood back west which are all over california are in holes somewhere then NCR would be back to using gold coins.
Brotherhood and NCR have not always been enemies. It was not till they came across the Hoover Dam did things go bad. Fallout 2 there is a brotherhood bunker in NCR's capital. Brotherhood used to trade openly with outside caravans. I don't see it as a fight to the death. If someone on either side wanted peace I am sure they would be willing to talk. It would not be something like the war between NCR and Legion.