That's if you see Logan (the movie) as in the tradition of the revisionist western. But it clearly wasn't. It was explicitly in the tradition of Shane, which appeared and was quoted in the film itself, in that Logan is a protagonist who may have used violence for ambiguous or ugly purposes in the past, but in the context of the film itself, either uses them in self defence or to protect others who need protection. Granted, Logan isn't the prettiest of protagonists in the movie, unlike Alan Ladd
Granted, Xavier brings destruction on an innocent family by seeking refuge. Granted also, that Logan is set in a post apocalyptic world in which the ideals and the family that Wolverine appeared to fight for are long since gone, and even mutants are almost gone. But the film ultimately ends on an idea of hope, that although individuals may die, not all is lost, and that hope can be rebuilt through sacrifice. It may not have been a message that you were interested in seeing in a film purportedly inspired by OML, but it was far from an incoherent movie.
Logan, I agree, borrowed very little from Old Man Logan apart from the idea of an old and declining Logan engaging once more in violence. But that's fair enough, because I am not convinced that Old Man Logan borrowed that much from Unforgiven except for a tradition of violent aging badassery either. Logan as a character who cannot escape his past doesn't colour every portrayal of Logan since his use in the X-Man... that
has been in Logan since he featured in the X-Men, after his brief appearance as a Hulk antagonist. At the end of the story, he rides off to kill more villains - and it's not as if the killings he has already committed in the story weren't portrayed as being justified or cathartic. (OML incidentally has some beautiful art, but it's not Millar's best story for DC or Marvel, which in the context of this debate would in American comics arguably be Red Son, which indeed has some interesting things to say about Superman
)
And justified violence, for what it's worth, is the key difference between Unforgiven, and Logan and OML. All the violence in that film is shown as being corrupting and futile, even when purportedly righteous (such as when Little Bill kills English Bob). I wouldn't quite accept the idea that Unforgiven deromanticised Westerns, though, but it's possible that we may understand different things by that word. While Munny wasn't a morally admirable outsider he was still, in the end, portrayed as an unstoppable force of mythic violence, the genuine "Bad Man" who the writer in the movie had been searching for. In getting rid of Shane in short, Unforgiven still had a place for Jack Wilson.
That idea, as interpreted by Ennis and Millar and many others, is perhaps the true legacy of Unforgiven - and a somewhat ironic one at that. An earlier revisionist Western, Dirty Little Billy from 1972, went much further than Unforgiven, in that everyone involved was portrayed as a squalid imbecile. But I have to admit it wasn't a particularly entertaining film - or even accurate to the historical figure of William Bonney, by all accounts.