To me, Nynaeve is the character introduced by the Pattern to heal so much of the damage that has been done. She can heal the removal of the Power and now she can heal the Taint. This makes a lot of sense to me. They couldn't do it during the AoL because the Pattern did not require it then, but now the healing of the Power is needed so the Pattern gave her these abilities. I think it is also why she was a wilder, not found until she had her own ideas about what can be healed and what can't. She wasn't raised in the Tower being taught what can and can't be done, she truly refuses to accept limitations on what can be healed. She won't accept that something can't be done until she fails to heal someone who has been dead for a week.
Just my two cents, but it makes sense to me.