As Demetrios pointed out, there were no longer any proper Mongol successor states left in the former Ilkhanate, whereas the other three divisions do have these successor states. Furthermore, the Timurids both eclipsed and claimed Mongol legitimacy within the former Ilkhanate, making them the logical choice for anyone wanting to do a Mongol Iran restoration game.thats not the point the mongol empire divided into 4, 3 of them are present in the game i just talk about the 4th. why not, doesnt it make sense as yuan chagatai or golden horde?
As a sidenote, I didn't actually know that you could restore the Chaghatai ulus.