I have a different problem with the sound than you do, OP.
So much loving craft was put into making the visuals mimic a 1920s/1930s cartoon, but not nearly as much attention was paid to the sound. The game looks like an old cartoon, but it doesn't sound like one.
In actual cartoons of that era, the music was a big part of the storytelling. Go watch old Looney Tunes or Tom & Jerry and you find that the incidental music was always a character in the action. Rather than just being an ongoing track, it would accompany and react to the actual action on screen. Accomplishing that in Cuphead might have been a lot more difficult, but other games (like Rayman Legends) have accomplished it.
Additionally, the music should have had a muffled filter applied to it in order to mimic what you hear in old cartoons, along with significant popping and hissing (you can hear this in between scenes but it seems to vanish during actual gameplay). As it stands, the music sounds practically CD-quality. Yet the sound effects have the muffled sound I'm looking for, so it creates a huge inconsistency in the sound design.
Additionally, it feels to me like the style of jazz they used doesn't really fit the era.
This game is such a love letter to old cartoons visually, but the sound just doesn't come nearly as close. It's not going to prevent me from playing of course, but I just think they underestimated the importance of incidental music to the illusion they were trying to create.