The NCR listens to reason more then any other faction. House wants to set up a libertarian dictatorship, Independence is saying "independence for the Mojave" while it's actually a military-forced dictatorship that refuses to call itself a dictatorship, the Legion is a close-minded, imperialistic, sixist, xenophobic, racist, raider-slave army where the only one who has freedom is the big dog on top that tries to pretty it up with crappy logic of "everything is worse and I'm only doing it to fix things"
The NCR goes into the Mojave and helps people. It sets up farms, it sets up trade, NCR supply corps wanted to give food to the locals for free, it rebuilds two power plants and brings wealth to the strip. Saying it needs to be "humbled" by losing the Mojave war is far from true as the war was already being heavily criticized by many of the NCR's citizens and trying to go into another war would just cause more problems until the NCR rebuilds.
Spoiler Hell, the NCR is also willing to let the Great Khans leave New Vegas and are willing to make a peace treaty with the BoS to the point they're willing to give up all their scavenged power armor. That sounds like listening to reason to me.
On Maxson listening to reason, that's not really all that well founded of an argument. You say he doesn't listen to reason, what is reason? Is reason just what you think it is? Maxson is coming in and taking out raider bases, super mutant bases, feral-infested areas, bringing in protection for the local caravans, building up trade and generally helping the people. Is "listening to reason" going easy on Synths? Synths have yet to prove they are anything more then a tool that is used by the Institute to anyone in the commonwealth the only reason Nick is trusted is because he is pretty obvious about who he is and even then everyone keeps him at an arm's length about things. To most people Synths are nothing more then a human looking Mr. Handy and for all we know that could still entirely be accurate.
Again I've stated this before, the synths could not be A.I.s at all and just be S.I.s, they're built to resemble actual personalities but can't actually break their coding just like the S.I.s in Old World Blues. Should we consider the S.I.s as people just because they have personalities? Just because they want to be free doesn't mean a thing, that could be a personality quirk or a glitch in their programming plus once they are free they're injected with fake lives, fake memories.
You said the BoS don't think with reason or can't be reasoned with but you don't say what "listening to reason" is or why your idea of reason is the one that tops all, you're working of "reason" is based on little information of what a Synth is (something we really don't know much about) and your own opinion of what a synth is. It's not wrong but it's not necessarily right is what I'm getting at.
But they don't lack any intelligence of what a Synth is because for all we know what a synth is is exactly what we're given by the BoS and Institute. Nothing but a human-looking Mr. Handy. The Institute isn't bloodthristy no but they're the reason for a lot of pain and misery as well as paranoia in the Commonwealth. The Institute kidnaps and replaces people, the Institute destroyed an entire town, the Institute made everyone afraid of their own neighbors, hell their own family, the Institute made the super mutants (though I don't believe the Brotherhood knows that) and the Institute is responsible for a lot of problems in the Commonwealth.