We need to talk about Rand.

[Randommer]

To me the debate seems to be closed - RJ said directly that Rand had turned to the Shadow in past lives.

 

And as to whether or not he's always the CoL, it does seem that way. As in, we have no evidence that the role ever falls to anyone else, and we have plenty of evidence that it falls to Rand fairly frequently, even after he has apparently betrayed the Light before (for whatever reasons). It is theoretically possible, at a stretch, that someone else could have had the role in the past or could in the future, but we have no particular reason to think it, and it's sort of irrelevant anyway.

 

It's his current powers, the ones we know for sure he has and are weird, that are more likely to be interesting in AMoL.