^
With the Klingons being a heavily martial culture that reveres war the idea of a Federation-Klingon War makes sense.
"Makes sense" or "is obvious?" Why settle for the obvious?
"Errand of Mercy" does have Kirk describing the Klingons as a culture for whom war is a way of life, but does that mean the UFP was fighting with the Klingons, or that the UFP was trying to intervene diplomatically while the Klingons waged war against other, neighboring worlds? Or that they were walking a Cold-War tightrope trying to limit Klingon power and expansion without pushing them into an open war that the Federation couldn't afford? There are many possibilities. And historically
Star Trek has done more stories about avoiding or ending wars than waging them.
In fact, the idea of a Klingon-Earth conflict made more sense on ENT than a war with the Romulans, from what we saw on the show.
Does it? The Klingons had their clashes with Archer, but it didn't seem they were as dedicated to large-scale expansionism and conquest as the Romulans were, certainly not in such a focused way. My impression of the ENT-era Klingons is of a smaller power, one that hadn't expanded very far yet despite being only four days' warp travel from Earth -- or at least was fairly easily prevented from expanding in our direction by the presence of the Vulcans. They were martially oriented as a culture, but the Romulans seemed to be a more organized, determined threat.
The Klingon War on DS9 didn't get that much focus so I don't think we've seen a full on war. It was used as a run-up, whetting our appetites for the Dominion War. The Klingon War was short and got short shrift.
Good. The shorter the war, the better. The Dominion War went on a season too long, if you ask me. They should've ended it after the sixth season and devoted the seventh season to the more interesting story of dealing with the aftermath and consequences of the war.
And perhaps the challenge of taking a familiar trope and doing something fresh with it.
It's been done so many times in recent years that I don't see the point in going back to the well so soon.
Also, the joy of filling in some Trek history, if the war took place in some of the aforementioned projected timeframes.
The word "joy" does not belong in the same sentence with the word "war." War is the ugliest thing imaginable. Surely there must be more fulfilling things to fill in that history with than just a lot more bloodshed and death and pain and horror. There's been more than enough of that already.
Star Trek is supposed to be a better future, a future we'd want to live in. It's valid to include the occasional dark time as an exception to the rule, if there's a good enough story reason for it. But it shouldn't be overdone. Too much war and disaster and
Star Trek ceases to become a desirable future. And then it would be no different from all the gazillion other boring sci-fi dystopias out there.