I agree with the original post. There's so many things wrong with the character now. Where to begin....
I suppose first off we could discuss how the character has mutated (hah!) since his first appearance, but before we do that we should look at the general idea behind the "All New All Different" X-Men roster. It's really obvious what the team was all about circa Giant Size X-Men #1....each character (and their powers) was sort of a personification of the archetypal "spirit" of his/her country.
A...stereotype, if you will. I know a lot of people think that's a bad word, but let's not kid ourselves. That's what they were.
Nightcrawler was from Germany, so he was the sort of devil/gargoyle/imp-type thing you might see carved in a cathedral, or perhaps something from a Brothers Grimm fairy tale.
Banshee was from Ireland where one of the most famous of Irish folkloric entities was the shrieking banshee. Not as obvious as patterning a character after a leprechaun, but that's probably for the best.
Easy enough to figure out what Colossus was all about. Russia was big, powerful, and how many reels of footage of Russian tanks, foundries, factories (ie steel stuff) from Stalinist/post-war USSR have we seen?
Storm - rain goddess from Africa. Don't know what else to say about that. Makes sense.
Thunderbird - they must not have been able to figure out a good power for the Generic Indian so they just made him super-strong/fast/etc. Not very imaginative, which is probably why he was killed off so quick.
and Wolverine....
Wolverine's original character was informed by 2 things:
1. Where he was from:
He was from the mountains of Nowhere, Canada. He was a rugged
rustic, in-touch-with-nature, woodsman-type. A mountain-man.
2. The animal that inspired him:
Wolverine's were small and vicious. It was thought they were so mean
that they could fight off bears...so mean they would even continue to
fight and kill when they were wounded - just like the character.
Pretty simple stuff, but once Wolverine started to get popular, writers apparently forgot what he was all about.
He's no longer a crazy, mean little mountain-man. Now he's drawn like some suburban kid's conception of "rebellious cool". I've seen him drawn in a Harley-Davidson shirt with a black leather jacket and cowboy boots. I've been to Nowhere, Canada and met crazy survivalist types....they don't dress like that. Now he seems more like a "tough urban biker from the wrong side of the tracks" rather than a berserk little hick from a place hundreds of miles away from any "tracks".
Wolverine isn't a personification of the Canadian wilderness anymore so much as he's a pretty-boy extra in a Velvet Revolver video, which is totally bass-ackwards.
On the super-healing: It seems clear to me that the idea behind his regeneration was so you could justify his being able to fight while wounded and bloody (like the real wolverine was thought to do) - if he's constantly healing really fast, then he can keep going despite injuries and wounds. Of course the healing power has been scaled up to the point of lameness.
The Japanese connection & the whole "fallen samurai" thing - I know this goes back to that 4 issue limited series from the early 80's, so it's not exactly a recent thing, but I still think it's lame. It'd be like giving Banshee, the quintessential Irishman a background as a Mexican bandito - just doesn't seem to fit with the original concept.
And finally, Wolverine's "cool badass-ness" is just sold way too aggressively for him to be anything but irritating.