One of the pratfalls of having Jackman as Logan in all of these X-Men movies is that he's shown up in every timeline that can possibly be imagined for these characters. With X-Men: First Class, they shot back in time to present vintage Logan at the start of Charles Xavier's school for mutants, and in Days of Future Past, they sent him even further back. Logan, meanwhile, will jump ahead to a dystopian 2024, when the destruction of the world is underway at the hands of an evil, mutant-hating corporation headed up by Nathaniel Essex, a.k.a. Mr. Sinister.
In essence, Logan has already covered all of the temporal bases this franchise can possibly touch upon for Wolverine, so there's nowhere for him to go from here except forward. Since Jackman is stepping away from the role after this, he won't be around to carry that torch into the apparently bleak future, and who could possibly replace him as grown-up Logan? There's no precedent for giving him a new face (this isn't Batman, a character that a slew of actors have played; this is Jackman's character, through and through).
The possibility of pulling a Han Solo maneuver with a prequel seems precluded by Jackman's own appearances throughout the past timelines, too. Whereas the X-Men: First Class series managed to reinvent the characters with a younger cast to look back at their early lives, Jackman stuck around. Besides, he's already handled his own origin story. So, while there's still a chance that Logan could walk away from his final film unscathed, the only real way to get any closure would be to kill him off and let him go for good…because otherwise, fans will likely keep beating Jackman's door down to come back for more.