Witch's Homework and Surpassing Fate
the part about it having to be delivered by the traveler implies that the witch's homework stuff needs to delivered by them for it to have an effect, the traveler is the required "formality".
So maybe the witch's homework makes characters stronger by letting them surpass what is allowed by the hp's designed fate, and thats why the traveler is needed, a descender not controlled by fate, who can change the fate of the world and the ppl within it, an
Nicole makes it clear that once a persons homework is done their story is inscribed in the witch's dictionary. So if it is abt evolving them past what their designated fates have in store, then the witch's dictionary could be writing that new fate into the world, like how Durin needed to write his story into teyvat in his story quest.