Are there any games in which the GM levels up?

Are there any games in which the GM levels up?

Are there any games in which the GM levels up?  Why should the players have all the fun of getting new moves and more interesting things they can do as time moves on?

There doesn’t seem to be a mechanical way for GMs to get better at GMing, it’s just letting loose everything you’ve got right out of the gate.

Why haven’t games been codifying session moves?

Why haven’t games been codifying session moves?

Why haven’t games been codifying session moves?  I mean, there are GM moves, player moves, monster moves, but session moves are a thing too.

Apocalypse World has love letters and countdown clocks.  Dungeon World might have a custom monster, or dark portents.  There are custom moves that are only meant for one session, and questions you want answered/situations you want to throw at people (I’ve heard about Bangs from Sorcerer but haven’t read it).  These all seem like specific moves picked out for a session, split between the GM and players.

One thing that worked well was I created moves for a session (one for each character and I think a general one), put the triggers as public, and they’d find out the effects when they triggered it.  “Sketch, when you explore the derelict ship alone, roll +weird.”  “Whenever someone gets bitten by the jungle, roll +cool.”  It did a great job of driving characters towards things in the same way highlighting stats does.  Basically they were love letters that the characters could work towards, if they wanted.  And why wouldn’t they want to find what was hidden on the other side of that paper?

What other games have session moves?  Are they something that should be in games?