I'm frankly shocked that no one has said Lou Reed.
I'd noticed that, too. I think it goes back to what I wrote, above, about Ian Curtis' use of words. It sort of indicates that maybe a distinction should be made between lyrics and words. All lyricists write words for songs, but not everyone who writes words for songs is necessarily a lyricist. The dictionary definition I have for "lyricist" is very specific: "A person who writes the words to a popular song or musical". In my view maybe there has to be separate categories for writers of pop songs and writers working in rock music or the arty regions of pop/rock hybrids. Lou Reed, Ian Curtis, and others like Patti Smith and David Byrne would belong to the second category. Morrissey belongs to the first.
I think it's a valid distinction because Morrissey has clearly always tried to write popular songs, meaning songs to be played in the charts. There are specific forms for pop music, as we all know, and Morrissey's greatness lies in his ability to smuggle the unlikeliest words and ideas into traditional forms, as well as tweak the forms themselves. (He wasn't the first to try this; among post-punk artists, Edwyn Collins did it first, and many think just as brilliantly, and at any rate I think Bob Dylan was probably the original.)
For art-rock-pop hybrids, it's more writerly in a general sense, by which I mean the songwriter is using words in an unorthodox way to stretch the boundaries of the popular form until it becomes something else entirely. Not to say they're not riffing on the forms in some way or other. Lou Reed was inspired by surf rock and Chuck Berry, among lots of others, so there's a pop element in the VU's stuff. But he was also influenced by the Beats, Burroughs, and others, so there are lots of different elements in play. He would swing back and forth between writing classic pop lyrics and provocative poetry that didn't quite fit into any category. This was true of Patti Smith (whose story we all know by now), and she's a great test case because although the words to "Horses" are often fantastic, they're more writerly than the her one big hit, "Because The Night", which was a lyric written by Bruce Springsteen. He, too, was capable of writing in both modes. Same for The Doors, with the split between The Jim Morrison Poetry Hour! crap and the hits Krieger wrote, which someone else mentioned above. The difference is obvious.
So I'd say that Lou Reed and also Ian Curtis (a reader of Burroughs, Ballard, and Céline) are great writers who fall into the 'writerly' category. Morrissey was influenced by Wilde, Delaney, and several other writers, but I don't think they influenced his writing in the same way. He's always working within specific forms, usually to brilliant effect, which is why he's arguably the best lyricist who ever lived-- though at the risk of being repetitious, as I said above I do think the music played a larger role in that success than others do. Because if we use my distinction to narrow the field to pure pop lyricists working in a specific form, and it comes down to sheer intelligence, inventiveness, word-craft, and wit, Morrissey would be a distant second to Stephin Merritt, and we know that can't possibly be true.