Logan is the kind of movie that you can probably only do with a handful of characters, ones that are so established, popular and well-known that there is scope to subvert them significantly and for the audience to enjoy that.
The point of the movie is that we start with a 'broken' version of the character and we see him find his way back to the hero that we know he can be. We're rooting for him to become that heroic version of Logan again, but the story wouldn't be anywhere near as powerful without him having a deep hole to dig himself out of.
It's not that different to DKR or a lot of similar stories. Part of the reason these stories work is that we start with a version of the character that's such a departure from what we're used to do that we think "wow, how did it come to this?" - and then we can't wait to see how the character finds themself again. Very like the Old Man Logan inspiration really.
I'm not sure there are many other superhero movie characters who could bear that at the moment, but Logan really worked for me.