NOTE: I RARELY READ COMICS AND HAVE ONLY READ MAYBE 2 ESSENTIAL X-MEN COLLECTIONS.
Maybe it isn't fair, as a non-comic fan, to even comment. But after growing up on the X-Men cartoon, seeing all of the X-Men movies and watching a large number of comic movies over the course of my life... I think Wolverine is boring. Or, rather, I think Wolverine has been made boring by the fact that every character has become dark, angry and brooding. Wolverine initially offered a unique hero who had a different perspective - he was a loner among a group that bonded over the fact that they were all forced to be loners. Wolverine was the consummate outsider, the rebel among rebels. Fast forward a few decades, and suddenly virtue is boring and every hero HAS to be angry, flawed and dark, and basically a Wolverine clone, and it no longer makes sense to make him the central figure in everything.
Wolverine needs an upstanding, virtuous Cyclops to have a balance. If everyone's emo, then the character is diluted and meaningless.