An excerpt is good at giving an idea of the writing style and skill, but often doesn't really tend to tell me what the story is about (and thus whether or not I'd be interested in it).

With my fics, I often tend to take a line or two from the story as the summary, but I try to choose something that gives a good idea of the subject matter. (I don't think I always succeed.) Some people pick what they think is the best line, which again, may give me an idea of the writing style, but is not really telling me what the story is about.

(But then so many people in fandom don't use summaries as a way to choose their reading material anyway, and instead read based on pairing or author or kink or something else that is totally irrelevant to me. :p)