Rewatching Cinderella's Castle is... different
I loved it the first time! There's not a character that's uninteresting, and it's built around these seemingly undefeatable villains that give scenes a sense of constant tension.
Rewatching without that tension though, and I think the line pacing might be a bit strange. It's very "Let me tell you what's going on, now I'll SING ABOUT IT". Cinderella in particular tends to just start rocking out of nowhere.
Some songs matter a great deal, such as the goddess's song and the ballroom scene, but... it honestly feels like the singing was an afterthought to the acting, for better or worse. I think for the songs to matter, something needs to happen in the songs. Nerdy Prudes Must Die has the majority of its major story beats happen mid-song, which gives them weight. I think Cinderella's Castle probably needed a bit more of that.
The incredible puppet work (and having actors dressed as the human versions of their puppets) and solid acting across the board kept it together for me, but I think it would have been about as good sans songs.