This might have interesting implications in tWoK, as there is such a cultural taboo with anything about predicting the future (especially in Alethi culture). I'm guessing as the plot progresses we will see someone who will gain an ability to do such a thing and really struggle with it. We've seen Dalinar's struggle with similar things by seeing the past.
My guess though is that it would be someone like Shallan or Jasnah. Jasnah wouldn't have as big a problem with it, being a heretic already (any tension would come from her having to convince others what she is predicting is true, and then not being burned as a witch), but it would cause Shallan to really have a crisis of faith and inner struggle, so to speak (Navel-gazing is something that Brandon seems to play with a lot as a writer).
Perhaps another possibility is Elhokar, but he just seems too shallow at the moment for something that monumental...
I agree though with the above that it would seem almost universally that this ability is connected with either using the "body" of a deity or the power/influence of that diety, making me think that Stormlight and/or spren could fit in that category.