They didn’t just do parodies of music styles, artists, and songs, they parodied the whole concept of being a struggling rock star (or a struggling musician) and the associated difficulties of management, gigs, fans, and survival. That makes for some hilarious stuff.
The first usage of the word parody in English cited in the Oxford English Dictionary is in Ben Jonson, in Every Man in His Humour in 1598: “A Parodie, a parodie! to make it absurder than it was.” Flight of the Conchords does get quite absurd. According to the copied copies of Wikipedia (more simulacra), “A parody (also called send-up or spoof), is a work created to mock, comment on, or poke fun at an original work, its subject, author, style, or some other target, by means of humorous, satiric or ironic imitation.”
We need more humour in the world.