"Let It Go" may be a phenomenon associated with Frozen, but the musical Hamilton's songs. Utilizing rap and hip-hop alongside more traditional show tune stylings, the production's musical numbers brilliantly bring the story of Alexander Hamilton to life.
While Hamilton already has over 40 songs, making it one of the most dense musicals on stage in of lyrical content, there were several more that didn't make the cut when it moved over to Broadway. While it's hard to argue against the quality of Hamilton's soundtrack as is, almost all of the deleted songs are at the very least interesting, including solid wordplay and/or good character development, even without being fully necessary to the overall story.
One such example is "Let It Go", which would've been the eighth song in Act II of Hamilton, and would've came after the Off-Broadway version of "Schuyler Defeated", which was also changed in the finished production. In that take on "Schuyler Defeated", Eliza and Philip Hamilton interrupt Alexander while he's confronting Aaron Burr about his decision to run against his father-in-law for the Senate seat, with things between them getting heated. "Let It Go", then, finds an annoyed Alexander challenging Eliza on her getting in the way of his talking to Burr, singing:
"What in the hell was that? / What in the hell are you doing downtown? / Don't you know that Burr is going to run against your father to humiliate me and try to bring us down? / I will not let our family be embarrassed like this / I'll grab a pen and paper, let the whole world know / You swing at my family you better not miss / You better have another punch to throw."
Most of the rest of the song is taken up by Eliza and the returning George Washington trying to calm Hamilton down, or in other words telling him to "let it go" and to take a different approach to tackling his problem with Burr. Although it's lyrically yet another strong song, the number doesn't add all that much to the narrative that isn't accomplished elsewhere, and so the removal helps to streamline Hamilton's story somewhat. It means things can go straight from "Schuyler Defeated" to "Cabinet Battle #2", which is a better way of showcasing the various political struggles Hamilton was facing at this time, and that Burr wasn't the only issue to deal with.
However, while "Let It Go" was cut from the musical, it wasn't lost entirely, as Burr's aspects of the songs made it into "The Election of 1800", such as "Talk less... smile more... shake hands with him... charm her!" While it might've been nice to include, it also only works as a follow-on from the original "Schuyler Defeated", and it's arguable that's the bigger miss. While the version that did make it still works, this would've made the hostilities between Hamilton and Burr even clearer, made a little more sense in of the story (it doesn't really fit that the Hamiltons learn of Philip Schuyler losing his seat when it happens, whereas the original has them discovering Burr is running for it), and also teases the death of Burr's wife, Theodosia, adding greater emotional weight to his journey. It doesn't derail the musical by any means, of course, but it does make it more of a shame that Hamilton had to let these songs go.