Logan is a Western.
Its visuals, its tone, and its narrative all fit pretty classic Western iconography, and it’s clear that James Mangold isn’t afraid to beat you over the head with Wild West imagery and references to older movies if that’s what it takes to drive home the point that this is a cowboy flick, not a superhero movie.
One of the conventions of the Western genre is an overwhelming abounding feeling of isolation. The point of the Wild West is that the law can only be enforced by the guy with the most guns, and so when a lone hero is up against a vindictive posse of outlaws, he doesn’t have the option to go seeking out help from friends or allies.
Or, for example, from his ageless regenerating brother who has bone claws coming out of his fingers.
That would somewhat ruin the whole narrative of the story.
According to Hugh Jackman, there was consideration at one time that Sabretooth (the version played by Liev Schreiber in X-Men Origins: Wolverine, not the glorified punching bag from the original X-Men) might appear in the film, similarly aged by time, in order to help his little brother out:
“There was a moment when we were thinking about, as I recall, Jim [Mangold] had an idea where when they were on the run, and they go to the gambling town, there may have been at that point they were going to see [Sabretooth] for help. He was going to be there for help. Now that you mention it! I wouldn't swear to it, but we thought that would have been an interesting thing to do. And then for whatever reason we didn't do it.”
Presumably the reason they didn’t do it is because it would have ruined the movie.
Logan works so well because there aren’t dumb cameos from mutants we don’t care about dotted all over the place. We don’t have to sit through a dull subplot featuring Warren Worthington III’s daddy issues, or pausing in the middle of a movie for Wolverine to have a boxing match with the Blob.
Logan has exactly the right number of mutants, and any more could have jeopardized the film’s isolated aesthetic.
At the same time, it makes sense that director James Mangold considered putting in Sabretooth—after all, the entirety of Logan is about familial ties and responsibility to kin.
Perhaps, though, somebody heard that the director was floating this around, and subtly leaned in to tell him that Sabretooth isn’t actually Logan’s brother in the comics, that was just a fan theory which was floating around while X-Men Origins was in development.
At this point, Mangold presumably flipped out, threw all his papers out the window, and started afresh.
At least, after pausing briefly to consider the possibility of a Wolverine/Sabretooth makeout scene which wouldn’t be quite so creepy if the two characters aren’t related.