For Narendra III to plausibly be a single turning point that so easily changes things, we need to have a long history of animosity and almost-wars, which we do indeed have. I do think it's safe to say that the first Khitomer Accords were basically just a cease-fire, not a treaty of alliance of any kind. Basically, a promise to leave one another alone and probably some one-time industrial assistance from the Federation to the Klingons in exchange for something the Federation wanted.
I think it's also important to remember that the Federation/Klingon conflict was long a metaphor for the Cold War. Fundamentally, the Federation and Klingons have completely opposing ways of life. The Federation largely thought of the Klingons as brutes, and the Klingons largely thought of the Federation as honorless weaklings. The Klingons, being the more aggressive, would need to be the ones convinced otherwise first, and I doubt a cease-fire would do anything to achieve that.
What's interesting to me is that Starfleet knew the Enterprise
-C was lost near Narendra III, but didn't know about the Romulans. Just how did the Federation think the C was lost? And who did they think destroyed the Klingon outpost? I could easily see the Klingons finding out about the C somehow, and accusing the Federation of destryoing Narendra III. The Federation, of course, would deny it, and probably begin to suspect the Klingons destroyed the Enterprise.
I mean, think about that a second. You're a Federation citizen, and you hear that the Klingons are accusing one of your ships of destroying one of their colonies, and it's the Enterprise
! Not only that, but she was lost. "The bastards probably destroyed her. They've hated the Enterprise
name ever since that Kirk guy showed them what idiots they are." With that kind of mutual accusation and suspicion, I think war was inevitable.
And just what were the Romulans doing? We know that the Romulans attacked at least one other outpost during this time, Khitomer. It appears that there was bad blood between the Empires since the original alliance, and yet the Duras family was eager to cooperate with the Romulans for their own gain. Did the Romulans then know that if they could attack colonies along the border they might be able to destabilize the situation between the Federation and Klingons? War between her two greatest enemies would surely only benefit the raptors. In the Prime timeline, perhaps the Khitomer attack was another attempt at doing the same thing they tried to do at Narendra III. Perhaps in the altered timeline, another attack wasn't necessary, and thus no Worf in Starfleet. Then again, perhaps there was an attack on Khitomer and it made the situation that much worse.
All wars must have an eventual victor, though. Between the Federation and the Klingons, who would the Romulans really want to come out on top? I would wager the Klingons. Though they probably see them as violent brutes, I would argue the Romulans would say they are dumb enough to be manipulated where the Federation is not. Therefore, there's a likelihood of the Romulans providing some material assistance to the Klingons through channels such as the Duras family, but remaining officially neutral. The raptors become vultures.
Add to that the fact that Starfleet is consistently depicted as widely dispersed. If I had a nickel for every time the Enterprise
was the only ship in the <insert space measurement unit here> I could buy my own Enterprise
. Then, add the fact that we appear to see great growth in the Federation during the early 24th century, and the other conflicts we know were ongoing; Cardassian, Tzenkethi, and possibly Tholian per "The Icarus Factor." As others have said, Starfleet was probably over-extended in her commitments during this time, awaiting a straw on her back to break her.
Technologically, the Vor'cha
class visually suggests the Klingons benefitted from their alliance with the Federation. Does this then mean that the Empire's warships were inferior? Perhaps. But technological superiority certainly doesn't guarantee Federation victory. Klingon ships are oriented primarily for war, where Federation ships historically were not.
And let's not underestimate the Klingons themselves. These are a people who glorify conquest and death, and who by their very way of life embrace war and fighting. The Federation and Starfleet, though I by no means believe them to be the extreme doves they are sometimes depicted to be, are reluctant to face war. The Klingons are vicious
. Kamikaze tactics in the face of defeat are established, notably per Worf in "First Contact." Even if Federation ships could overpower Klingon ships technologically, the Klingons would surely take their vengeance in almost every lost encounter via kamikaze tactics.
And I would also throw out there the fact that "twenty years of war" doesn't have to mean that they were in open war for all of those years.