The problem is that Exalted, at least in First Edition, isn't a game about the heroes succeeding at the impossible. The reason the journey of the young Solar circle to recreate the First Age seems so impossible is that because in the original conception, it is. It's about how mythological heroes are awful, and the creatures of legend would be as villains to modern people-and how by trying to win glory and shape the world to their liking, they fuck things up and ruin things for everyone.
Exalted is a game where the heroes are expected to fail. That's the original ending way back when the first edition corebook was released. The heroes fail. The godlike might of the Solars does not fix the world, but only breaks it more, to the point when the old gods use them again as a desperate Hail Mary to keep Creation from permanently ending four ages later, they shackle the Solars to the point where their powers are completely useless against a random thug with a gun. The Lunars spend so much time fucking animals rather than leading that they die out, leaving only races of degenerate rage-filled Wyld-maddened beastmen to burn down the last vestiges of civilization because they're crazy. The Sidereals fuse inexorably with the Loom and multiply their shards a millionfold in a desperate attempt to keep Creation going-and even that fails, creating a world where the mad whims of men lead to even more corruption and taint the best-intentioned workings to save it.
Even if Exalted has officially split from the World of Darkness, this original envisioning of Exalted is actually very important. And that's where "No Takebacks" fits in. No Takebacks- because you're doomed. No Takebacks- because your actions are supposed to damn the world, and by the time you realize that, you can't change a thing about them. No Takebacks- because your characters are supposed to fuck up, and fuck up so badly, that Four Ages later, the gods absolutely refuse to let you have even a fraction of your old might.
Exalted has changed and evolved from a game since then, yes, but the whole idea that if you fuck up, the world is doomed to decay and sorrow is still a core part of its identity.