I love this thread so much, because I'm in the musical theatre industry and half of the suggestions here are what we would consider audition warhorses in that world

It's really interesting to see how different music speaks to different groups/purposes.
From musicals that are "overdone" in our world but not in the skating world, I'd definitely say Wicked, Thoroughly Modern Millie, Evita, and Gypsy. Carousel and South Pacific also have really beautiful scores that I don't see much of. She Loves Me has a wonderful score with lots of character-y songs like "Vanilla Ice Cream" and "She Loves Me" (This Tony Awards
medley has a pretty good selection). The Cole Porter songbook has a ton of great, jazzy selections, especially the scores of Anything Goes and Kiss Me Kate.
From more "obscure" musicals, I definitely second the poster(s) who said Aida and Ragtime, and I would add Waitress ("She Used To Be Mine" and "You Matter To Me" are great ballads, and "Bad Idea" would make a really fun dance/pair program). I think "
Charming" or "
Dust and Ashes" from Natasha, Pierre, and the Great Comet of 1812 could make really interesting programs for singles. I think one or two teams might have used it already, but any of the music from Once would also be beautiful.
Regarding some of the more recent hits, like Dear Evan Hansen and Hamilton, I actually don't think they'd make great programs. With the exception of the two Aaron Burr songs ("Wait For It" and "The Room Where It Happens") and possibly "Satisfied" or "Burn", Hamilton is so rap-heavy, rhythmically complex, and story-centric that it would be hard to skate to. Dear Evan Hansen is a very, very poppy score that doesn't strike me as very skateable either. Stuff like DEH, Next to Normal, and Spring Awakening seems more suited for a show program than a competitive one, if at all.