Why Moirraine? (Spoilers, be warned!)

I have to admit to some really serious confusion here.

Don't get me wrong, I love Moirraine.  I loved her Gandalf-esque way of leaving the party.  I love her calm solemnity, and her caring nature.  I'm actually really upset that she did not get to see Rand at the end of the book; why couldn't her AND Cadsuane have seen Rand canter off at the end?  Between her and the soon-to-be Amrylin, I think Moirraine deserved it more.  She also deserves the Stole and Seat more too, but that's another gripe.

But really, why, WHY was she needed in the cave confronting the Dark One?  Nyaneave makes perfect sense; Immensely strong, helped cleanse Saidin, but why Moirraine who is far weaker than she was before?  Nearly anyone else could or should have gone in, particularly someone more powerful to make using the angreal even more potent.

I really just don't get it.  I'd love to hear everyone else's opinion on this too!