I'm just wondering why Wolverine does not appear in his iconic costume when even in
The Wolverine, there is apparently a deleted scene to show such a costume?
This deleted scene can be scene in the DVD/Home Release extras.
Director James Mangold explains why it wasn't used in The Wolverine:
So one reason is corporate politics and professional respect.
The second reason is that only comic readers or cartoon watchers, established fans who know of Wolverine outside of the Hugh Jackman movies, would recognize the suit. Everyone else was confused even through its clearly a suit and mask.
The last reason is that the fan nod would cause problems with the stinger teaser that leads up to DOFP.
So, now that we explained the The Wolverine alternative ending, the reason they never used the classic suit in the rest of the films is basically the same thing.
Only hardcore fans would know about it, while it would clash with the rest of the stylistic choice they made for all of the X-Men, as covert agents. They intentionally moved away from the colorful individualism of the X-Men suits, and went with a Uniform, literally meaning One Form. As the joke goes in X1:
Funny enough, First Class forward returns to individualistic costumes, as the X-Men get more established in the new timeline. The old timeline forced mutants underground, but the new timeline of DOFP, having a mutant publicly save the President of the United States, has prevented the X-Men from needing to be a overly militaristic group.
Well, mostly because the costume is a bit ridiculous when taken out of the context of four-color comics. Might as well ask why Logan's hair doesn't stick out to both sides as much as it does in the comics: just because something works, visually, in the medium of print comics doesn't mean it will work in the medium of live-action cinema.
As @AnkitSharma mentioned in the comments, the deleted scene is probably a nod to comic fans who have a sentimental attachment to how Wolverine looks in the comic books. But in any adaptations changes must be made, and visual and aesthetic changes most of all, to fit the new medium.