"Let It Go" is also very easily quarantined into a musical-theatre box which those Elton recordings weren't. They were written and recorded by an adored pop star with a decades-long career and a history of Grammys. And they weren't the actual vocal tracks from the musical but the re-recorded pop ballads. And that tradition includes the pop/R&B cover of "A Whole New World" that won, as well as "Somewhere Out There" which won Song of the Year in the 80s from AN AMERICAN TAIL.
These are similar, but not analogous. If Beyoncé covered "Let It Go" on the FROZEN soundtrack and that had radio play, that would be nominated in the General field categories.
Words don't deserve that kind of malarkey. They're innocent, neutral, precise, standing for this, describing that, meaning the other, so if you look after them you can build bridges across incomprehension and chaos. But when they get their corners knocked off, they're no good anymore…I don't think writers are sacred, but words are. They deserve respect. If you get the right ones in the right order, you can nudge the world a little.