Early freestyle rap was written down, but since 1990, it has focused on improvisation, or "coming off the top of the head". If people in Real Life can learn to improvise verse, it wouldn't be impossible for a culture to value the ability to improvise verse. Musicals and blank verse plays take place in such a culture. As for the tunes, a lot of Emily Dickinson poems can be set to the same songs because they're all written in "ballad meter", or iambic heptameter. Perhaps there are a few tunes that everyone knows and can employ in an improvised Filk Song.