[AlanC]

I'm going to go counter to the usual wisdom here and say that shoe trees serve the same purpose as a woman's hair curlers: to hold the "set" of the shoe (or hair) as it dries.

I think this is the primary purpose as well. Shoe trees can actually help creasing over time if they are put in promptly after they are worn.

I don't doubt that there is some absorption of moisture, but filling out the shoe itself is the main function.