For me, it isn't the fashion for hyphens that's annoying. In an odd way, I've always felt that the attraction of hyphenated names was that they emphasized the Americanness not that they emphasized the ancestral/original culture. Before the rise of the Hyphenated-American terminology, identifiable immigrant groups simply got called the pre-hyphen label, as if they were only their ancestral/original culture and didn't count as unmarked Americans at all. "You're not an American, you're Polish; you're not American, you're Mexican; you're not American, you're Chinese." I think the hyphenation is a bridging state that acknowledges the residual insistence on seeing them as the marked case (the infamous conversation of "I'm an American" "No, what are you really? Where are you from?" "I'm from Chicago.") while putting the hearer on notice that they claim membership in the larger American culture. (Sorry about putting this all in X-American terms, but it's What I Know.)

The hyphenated labeling may well be a symptom of the same underlying situation that enables the annoying disnification of ancestral cultures: i.e., a general acceptance of individual multiculturalism and the claiming of it as a positive trait rather than a flaw. But I think it's because there has (in the last half century) been a rising view of individual multiculturalism as a positive trait, that there are people (and especially people who can pass as "unmarked-American") who seek out an artificial personal multicultural identity in order to participate in what they see as a richer status.