This needs some investigation. Discuss ideas and findings on the talk page. Specifically: Is the animation actually broken? Test it out in-game.
To do:
Properly render these animations by removing parts of the model that would not show up in-game (see the bone visibility animations). Of note, the rope is around her waist for most but removed for the falling animations, suggesting it should usually be there.
Add the rest of the animations and fix this section's wording/layout
Origami Peach's model (character/origami/O_PCH.bfres.zst) has unused geometry for a rope around her waist, lots of unused animations for different actions, and models for her transforming back into paper (O_PCH_Transform.bfres.zst, P_PCH_Transform.bfres.zst, P_PCH_Transform.Default.bntx.zst) with associated animations. These all suggest she once had a more extensive role in the game.