Notes & Combos
This one is for the deck purists who dont like their archetypes tainted by engines that would make the deck objectively better. The wincon is to activate our vanity's emptiness on opponent's turn and otking on turn 3. Surprisingly, even without the trap ending on the link-4 with a quick monster or s/t pop by reviving yoko or tengu respectively supported by hand traps can be quiet powerful. While you pretty much win going 1st uninterrupted with trap access, the deck has no way to deal with a board. This means you rely entirely on hand traps or board breakers going 2nd. You also still NEED Hajun to resolve since he's the only starter.
About the list, I play all the good Mayakashis, 8 ways to the trap and the hand traps are Crossout targets or Small World bridges. The deck is build to do exactly the synchro climb into link-4 with the trap. While Yuki-Musume arguably used to be the best target for Hajun, in this you always go for Dakki because there isn't much to send with Musumes foolish burial effect. I still play her because she can be an extender if Hajun gets negated and the Mezuki send can help otks. The Extra is only Mayakashis because y'all hate generics, no in all seriousness it's kinda hard to play around the Extra Deck lock in pure.
I usually play Mayakashi Eldlich rather than pure, but promised I would go for max rank when konami drops the support. Please also check out the other Mayakashi variants if you dont want to do the same combo over and over again. Shoutouts to the regulars in the Mayakashi channel on discord, you've been blessing my draws and coinflips today to make this work. Also, thanks for sharing the copium for the long time we've been waiting for these cards.
Replays
Master Duel ID: 041-553-658 if you're interested in replays

Is there any reason not to be running Zombie World in the deck, even if you want to keep it pure? Zombie World has no ties to any particular group of zombies, and the entire archetype of Mayakashis are zombies.

You can definitely run Zombie World if you want. With this list I wanted to get to the synchro ladder as consistently as possible so I didnt want to run cards I could brick on. If you do the synchro climb and resolve the trap you almost always win so there's not really a need for balerdroch and the top decks dont really care about their types. But once again this is supposed to be an example of what a pure list could look like. Feel free to change things.