a very fun worldbuilding quirk that would suit hazbin hotel is if the whole show operated on musical logic but was self-aware about it. there are elements of this already, like vaggie begging charlie not to sing and the sharks exclaiming "they're fucking singing?" after loser baby, but i think it would be even more fun if characters actively acknowledged when they hear strains of music coming in when a song is about to start, where demons who are new to hell have to adjust to the fact that at any moment, they might burst into song without meaning to, or get swept up in a choreographed street performance that someone else set off. people having their own unique leitmotifs that blend with others depending on their relationships or mood, duets springing up between compatible voices on the fly.
alastor's insistence on reprising or crashing other demons' songs being characterized as rude or untrustworthy because what kind of dick steals your own lyrics and sings them better? what kind of demon doesn't have his own tune? vaggie being exempt from the compulsion because she's an angel, but learning to find her voice for charlie's sake so that they can sing together. angel dust only ever singing backup vocals for val bc he's val's property, and then being elated when husk draws him into a duet where their voices have equal strength. the vees bursting into "spontaneous" trios as a marketing ploy. when people sell or lose their souls, their leitmotif becomes subsumed under the melodies of their contractor. alastor only singing his own theme when he's alone; charlie humming her motif constantly, no matter where she is. lucifer forgetting the lyrics to his songs the more depressed he becomes, and rediscovering them again when he reconciles with charlie.
just, hell with an inescapable, compulsory musical culture that everyone is aware of.