Because he doesn't.
Or maybe he does, just a little bit, because Gaiman sort of looks like a whole bunch of other dudes (and dudettes) who influenced Morpheus' looks.
Well, at least his face hasn't been explicitly stated to be based on Gaiman's.
Reading through canon (that is, word of gods - people who actually worked on The Sandman) sources, I couldn't find an indication that Gaiman was explicitly used as an inspiration for Morpheus' appearance.
There's one bit where Gaiman says about his motivation with Morpheus:
The inspiration for his clothes came from a print in a book of Japanese design, of a black kimono, with yellow markings at the bottom which looked vaguely like flames; and also from my desire to write a character I could have a certain amount of sympathy with. (As I wouldn't wear a costume, I couldn't imagine him wanting to wear one. And seeing that the greater part of my wardrobe is black [It's a sensible colour. It goes with anything. Well, anything black.], then his tastes in clothes echoed mine on that score as well.
From the afterword to Preludes and Nocturnes. That last part about wearing black had also come up in Gaiman's Tumblr
For the record, this is the black robe with flame motif Gaiman is mentioning:
Left - from "Sleep of the Just"; middle - from "Dream a Little Dream of Me" (Constantine even joked that he wouldn't get on public transport with Morpheus looking like this); right - from "Sound and Fury"; all collected in Preludes and Nocturnes.
But according to Mike Dringenberg (the inker and then penciller of the first 8 issues), none of the characters were copied directly from real people:
None of the characters are direct renderings of individual people; they're composites emerging from my memories;
I think there's only one character that has explicitly been stated to be mostly inspired by a real person - Death:
Left - Cinamon Hadley; right - Death of the Endless.
Coming back to Morpheus, he's never stated to be based on, or even to intentionally resemble Neil Gaiman. He was a sort of collage of many people the artist knew back then:
The Sandman himself is even more of a composite. Certain well-known people influenced the design -- his mop of hair came from Robert Smith and ballet dancer Farukh Ruzimatov was always in my mind for his dramatic physique, but face wasn't so much Bauhaus' Peter Murphy, but rather a type of English face, of which Murphy's is a shining example. That face can be averaged between Dirk Bogarde, as he appeared in the 1959 version of A Tale of Two Cities; the young Terrence Stamp of Billy Budd, and David Bowie in the '70s, with a dash of Syd Barrett.
As for his bearing, he's an amalgam of half a dozen guys that I knew slightly in the old punk/ club scene and didn't want to know any better: they were all tall, pale, beautiful, and serious sleazebags who used women like toilet paper.
Ibid; emphasis mine.
I can see Morpheus resembling the people Dringenberg mentions:
Left - Robert Smith from The Cure (image src); right - Morpheus from "Dream a Little Dream of Me".
Left - Robert Smith; right - Morpheus from "Into The Night", collected in The Doll's House (image src).
Left - Farukh Ruzimatov (adapted from src); right - Morpheus from "Sleep of the Just".
Both are fit, skinny, muscular (Ruzimatov is a ballet dancer), but it's not possible to see a direct resemblance - for one thing, there are no clear shots of Morpheus' body in the first 8 issues. Once again, it changes later in series, when the art becomes more abstract:
Morpheus from The Kindly Ones chapter 5.
Left and right - Morpheus; middle - Peter Murphy (adapted from src).
This one is the most well-known source inspiration. Here's what Gaiman has to say:
The original idea-model for Morpheus was Peter Murphy from Bauhaus. …and even that was after I’d described him a lot and Sam Kieth had sketched pages of faces, and we’d picked one. Mike Dringenberg went “Oh, you mean a Peter Murphy face” and we went, “Oh yes.”
Thank @Slytherincess for hooking me up on Peter Murphy. Goth rules!
Gaiman even mentions in his interview in The Sandman Companion that he also wanted Morpheus to have a rock-star appearance:
I wanted him to look like royalty. In the late 1980s, kings and queens were dressing and behaving like ordinary people, and I felt it was celebrities - and especially rock stars - who were our true royalty. I made some drawings with that in mind, and with the Sandman dressed in a black kimono I ran across in a book of Japanese design. I sent those off to Sam Kieth, who was the first issue's penciller, and Sam developed the Dream we see in issue 1. The Mike Dringenberg, who was inking the first issue, said, "Hey, he looks like Peter Murphy from Bauhaus." Dave McKean and I got some Bauhaus videos and immediately saw that Mike was right; and Dave ended up making the central image on the cover of Sandman 1 a Peter Murphy-like face.
The Sandman Companion, "Secret Origins - Origins of Dream", page 236.
The closest thing I cold find for Morpheus to resemble Gaiman was like this (the general shape of the face and all the hair):
Left and right - Morpheus, from "Sleep of the Just" (Preludes and Nocturnes) and Season of Mists chapter 3, respectively; middle - Neil Gaiman somewhere in 80s or 90s (src).
Neil Gaiman himself certainly doesn't believe Morpheus was modeled on him:
Q: You look very much like Dream of the Endless. Is this purposeful?
A: I don’t think I looked like Dream while I was writing him. Maybe it’s a similar phenomenon to the way people grow to look like their dogs.
From Neil Gaiman's Tumblr.
Q: I have just started reading The Sandman and I had a question. I know you said that Dream's wardrobe is based on your own but is his appearance based on you as well? I personally think the resemblance is uncanny.
A: I don’t think so. This is what I looked like when SANDMAN 1 came out, after all…
(Photo of Mike Dringenberg and me at the first ever Sandman signing, at Jim Hanley’s Universe. Note the non-existent crowds, and the piles of unsold copies of Sandman #1.)
From Neil Gaiman's Tumblr.
and, most recently:
Q: Did you intentionally make Dream look an awful lot like you?
A: Not really. I suspect we’ve grown to look more like each other over the years, like people and their dogs. I mean, at the time that that issue came out I looked like this (I’m the one on the right):
Notice that with all of these, some traits seem similar, but Morpheus doesn't really look like any of them. My point is, sure Morpheus seems to look like Neil Gaiman - Gaiman was there, he's the creator of the character - but he also looks like a lot of other people who influenced the artist at that time. And if one was to look at later issues, Morpheus looks even less like Gaiman or anyone mentioned:
He retains the basic traits, but it becomes harder and harder to identify him with any particular person.
But it's only fair to point out that some artists apparently did use Neil Gaiman for their depictions of Morpheus. Here, it's Marc Hempel, who illustrated The Kindly Ones.