Currently it's possible to extract a given number of characters, sentences, and the whole intro of a wiki page. It would be natural as well as useful to also allow to extract a given number of paragraphs.
When querying Wikipedia, for example, it happened to me several times already that I want to extract the first paragraph because all I want is a short introduction to the topic. The full intro is often too long, a single sentence isn't always enough, and two sentences is sometimes too much, and other times not enough. Paragraphs are natural semantic units, so if I want a concise intro to a topic, usually what I want is the first paragraph.