Oh, totally agree. It was an unbelievably powerful moment, and the first time I finished the game, I thought about it for weeks afterwards.
I just can't help but be bothered by the fact that I can't really feel like the plot justifies it as a narrative device. The things that happen are the hand lighting up and the ghosts of Sonia and Rauru showing up, and that's it. It feels strangely contrived. I've sort of tried to come up with my own theories. Like, the stone Link touched in the beginning of the game that gave him the Recall ability is sort of also giving him the ability to call back Zelda. Or that Rauru's arm simply is all-powerful and can undo a draconification, somehow.
In the end, I've kind of stripped it down to "the power of love", going off of "when I felt something, like a warm, loving embrace, I woke up", kind of how Zelda awakened her sealing powers in BotW, but a tad more far-fetched.