Rand is told by both Verin and Lanfear that the portal stones can take you to different worlds. These worlds are different from the real world due to the different choices that were made. Does it not stand to reason, that some where Saidin is not tainted by the dark one. If so wouldn't it make sense for rand to try to find how to get to this world, becouse there would be some to teach him and the Asha'man. It also stands to reason that some where there is a world where the taint has already been remove from saidin. Making it easier to remove the taint where rand is.