Ta'veren isn't "a power" - it's a device through which the Wheel is able to reshape reality to correct what as gone wrong in the weaving, and the fact LTT also was one has nothing to do with what happens around Rand now.

What happens is that on Dragonmount, Rand has rejected his fears and denial of death, has fully embraced what it means to be part of the Pattern, understands the beauty of Creation and its rules, and accepts them. He was faced finally with the choice the Creator had laid before him at the end of EOTW: You're the only one who can win this battle, if you choose to. Rand had to embrace Creation and decide if it was worth saving or not, before he could face the DO. He could choose to go to Shai'tan, he could choose it was time to end Creation and use the CK to put an end to it all, or he could choose that Creation must go on, and takr the right path to make it happen, which meant embracing life and death and having faith in the Creator.

Rand is the dragon, and the Wheel has given him what he needs to defeat the DO, but Rand had to accept fully his role as the Creator's champion, the Chosen One. Rand used to see LTT more than a little as a destroyer. LTT also saw himself the same way, blamed himself rather than Shai'tan for Ilyena's death etc. LTT had lost his faith before the end, believed the Creator had abandonned Creation, started believing that a simple man like him couldn't repair what God had created, that it was pure arrogance. Ishamael implied LTT had refused to embrace what he really was, that he had refused to embrace even the name Dragon. That is very likely why LTT failed in the end to achieve more than a partial victory. He didn't believe enough that the Creator had given the means to Creation to defeat Shai'tan, didn't believe strongly enough that he was the instrument by which the Creator would work, through the Wheel system. The Wheel could not use him as completely as it had to, to win a complete victory.


On the mountain, after experiencing first hand Shai'tan's own power, Rand has finally seen where he went wrong, that losing his humanity lead to disaster, and he decided that Creation must be saved, and he's fully embraced what it means, and his own humanity, and his role as an instrument of the Wheel. He no longer fights to make happen what can't happen, he no longer see himself as a destroyer, no longer seek to avoid pains nor the joys or life, he is no longer feats death, accept that he might well die soon and others certainly will in the fight, but that it is all worth it so Creation goes on, so that he goes on and experience life again. Rand has reached the same point, in his faith, in his dedication and his understanding of Creation and his own role as the Champion that Moridin had long reached as the champion of Shai'tan.

That's why the Wheel is able to work miracles where Rand walks. Rand said it best in TOM. He isn't there as a warrior, and the LB isn't his battle. Rand was supposed to become an inspirational figure, a religious figure, his coming was the warning to everyone to get ready because the Last Battle was coming, and the Wheel would need all of the Pattern to fight it, from nature that would provide food to the humans and animals like the wolves. Rand was to be a symbol of hope, the living proof that the Creator had not abandonned Creation, the magnet around which what needed to be sacrificed would be sacrificed (like what bounded people, prevented them from accepting reality) and around which everything would gather at the end. Rand's not a warrior, merely the vessel through which the Wheel can bring all of creation to defeat the DO. Rand has accepted this role now, that's why the Wheel is finally able to use Rand as he was meant to be used. It's not Rand who is bringing reality back to what it would be if Shai'tan wasn't twisting it. It's the Wheel that is finally able to do so, because Rand no longer fights against what he really is. Shai'tan's powers are already too strong for this to last, the reshaping of reality happens only around Rand, and the DO reassert its corruption when Rand is no longer around.

The best way to understand what goes on is to compare to to "madness". The whole world is unable to see Creation as it really is anymore, Shai'tan is making them see it through the eyes of madmen. It is there, because the world believes it is there. Rand doesn't see it that way anymore, and where he walks, people are able to experience reality as it really is again.

It is also pretty much like tel'aran'rhiod, where reality can be what you choose it to be. But just like TAR, if you believe in the nightmare, they can kill you. The DO is exactly the same way reshaping reality to his will. The stronger people despair, the stronger they believe the end his near, the more they lose faith in the Light, the stronger Shai'tan probably becomes. The method through which Rand decides to close the Bore may not matter as much as his faith that he's doing what needs to be done, and that it will work. In the end, it might very well end up being a contest of faith and will.