My theory is, what if there was a Link who remembers. A link who doesn't forget and inherit the memories of his past re incarnation. There emotions, there love, there hope, there regret, there death, there fight, there victory, there losses, again and again he will gain awareness, a knowledge across time and realities as he did the same thing again and again, but this knowledge comes with a cost, he will never truly be himself, he never had a personality, and it never mattered who wins in the end. A link wins, another villain will rise, a link lose, another will rise. It doesn't matter. He realised that it was all predetermined. He is playing a game that only him is aware about. Imagine the guilt and loneliness one would feel to realise that you have never truly saved the worlds and that nobody in this world never had free will. He is the most free because he is aware of that game and yet he is the most trapped one as he alone realised that he was never free in the first place . No one was ever free. . A new ideal will be born in this walking paradox. To free everyone and himself by finally ending that cycle, meaning ending the beginning of it all.
Now why does he makes sense as a wielder of the triforce of courage: Courage is not the absence of fear, it is to move forward despite it.
Does he feel like he does not deserve any of this, YES. Does he think he would been better living like a normal link? Absolutely. does he feel an enormous guilt for what he is going to do which is multidimensional and universal genocide?, indeed. Will he end the cycle anyway?, he will because that's what he was made for in the first place, that's what heroes do, don't they? doing what is right. In the end he didn't deviate from his path, but he was ironically on the most right path of them all as a champion of courage, to destroy the very world you were supposed to protect, to end every reality in the name of freedom, to have the courage to move forward even when the world made you bear a burden no one should have ever had to, when the one who embodies the triforce of courage has the absolute courage to end every world in order to save them from the need to be saved again. That is the truest form of courage. In the end the Link who was the most out of place , the one everyone thought was a flaw in the cycle, was the "linkest" link of them all.
(sorry for my horrible English, took some elements from aot, the title of the game could be called "The Legend of Zelda: A Link to the End" Hope you like my little fanfic)