If Anakin can survive having his remaining three appendages cut off and burned up beside a river of lava, I don’t see why Palpatine, the galaxy’s most powerful Force user, couldn’t have survived falling down a shaft. It’s not like Jedi don’t have levitation abilities. He could have just hovered onto a catwalk, skeedaddled to a shuttle have been long gone by the time the station blew up.
Jedi and Sith didn’t have levitation abilities, until TROS. That is the problem with the ST, they just invented new Force powers as they go. Even death and injury are pretty much irrelevant now. It’s become a story with zero stakes. Had JJ directed ROTS, Anakin would likely just have grown those limbs back.