I think there are a few reasons I get into this. Having a concise representation of what you need to know (with presumably another cheat sheet for the basic moves and such) reduces the amount of flipping through papers/books/staring at screens during play. It makes things more convenient if not everyone has a copy of the book. And during play it makes it easier to remember what you can do and pick what to use, since you've got it all at a glance. I also feel like the constraint in form forces moves to be concise, which I think is a part of the evocative-but-not-precisely-defined Apocalypse World setting feel.
So, I obviously was thinking about how you'd do something similar for Chuubo's. Here's what I came with for Gatekeeper, one of the bonus Arcs from Jenna's tumblr. Jenna's powers are pretty detailed, so it required cutting examples and various amounts of descriptive text from the powers. It also required coming up with a concise syntax for the overly-complex MP costs powers have, which I'd have to explain on the cheat sheet or something. But it still seems basically functional.
Apocalypse World does have a place in the book with some extra commentary, if you feel you need more, though it's pretty minimal. So I could imagine doing something concise for the playbook and having a longer version you could refer to in the book. But I do feel like that'd reduce player exposure to the flavor, examples, and guidelines, which would change the feel of the game, so I don't know if this would be the Proper Chuubo's Experience.
If I was actually doing "A Wish Chang'd World", I'd probably be inclined to go further in the Apocalypse direction. Instead of a strict arc ordering for powers, have them as moves you get more incrementally and with some control over the order. Simplify the MP cost structure, and maybe have an Invoke the Miraculous move that would give you options for discounts or speed-ups if you roll well, rolling +Arc so things would tend to get cheaper/faster/broader in scope as you advanced without needing to write it out per-move. (If nothing else, tracking when you last used each power seems like it could get annoying.) Basically, having miraculous powers randomly fail seems contrary to basic world principles, but there's precedent for variable cost and speed, and you could potentially add other similar options as well.
But anyways, I've been thinking about game design choices a lot lately, and for whatever reason the physical presentation of player materials seems to be something that I'm pretty into. And I'm sure that this will be useful as I think more about how I want to do things for Librarians.