The central word in Fabian's explanation is "sectarian". It's a word which is pejorative to the point of prompting the obvious question: What exactly are the sects? Well, this rather over the top remark gives a hint:
I advise ordinands that if they must use the “Nicene” Creed in their parishes, they might march about waving American and Episcopal Church flags, while their church wardens tear up photographs of the Mormon Tabernacle: these gestures would express the custom’s fundamental spirit, and employ beloved Episcopalian paraphernalia lately fallen into disuse.When I was in high school, we used to process the flags in and out, but I think that was mostly to soak up three more acolytes, not necessarily to make some sort of statement. It's the Mormon Tabernacle, though, that's the phrase to note. The Mormons are certainly among the excluded when put to the test of the Creed, and so are the JWs, and the Unitarians. Officially, though, that's about it. Oh, and the Orthodox, because of the filioque. But if we were to take that clause out, one suspects that the Catholics would object, so it's rather a "can't win" situation.
Meanwhile, in the irony department, the Episcopal Church is about to be converted into a sect of Anglicanism. There's more than one way to be sectarian, after all, and one of those ways is to break faith with the whole. And one of the American church's persistent problems is that there are clerics and even bishops who dissent from the Creed. We cannot, of course, reduce the sectarian walls between us and either the Mormons or the JWs, so there's no point really in trying. And there's no real reason to, unless you want to believe that it doesn't make any difference that the dogmas of those sects are in blatant contradiction to the Creed-- and to each other.
I'm not a believer in the theory that one can root around in the history of a practice and apply that history directly to the present. In particular, I do not agree that one can apply the meaning of the remote past as if it were intended in the present; that meaning must be found in the present, independently of the past. And it seems to me that the main power of the Creed in the present is unitive, not sectarian. The vast bulk of Christianity holds that it does matter what one believes about Jesus; repeating the Creed each week can be taken as an act of solidarity.
I'm not going to say that omitting the creed is in some way invalidating, and I'm not going to step up to the question of how well it fits in liturgically. And I'm not going to condemn the Gregorians outright for omitting it. But I wouldn't do it, and I would be uncomfortable at a parish were it was always omitted.