Eh, even if Anne was hit by a truck and woke up in Amphibia, I still don't think the story would have changed that much. Odds are she would still recognize that she's in another world and not dead, especially if her friends are there as well. Marcy might go a little harder on the whole 'we can't go back, we died,' thing, but Anne would still seek out Andrias in hopes of finding a way back, his ancestors would still be dimensional conquerors, he would still want them open the way to Earth with their powers. Because Amphibia was, in the early seasons, a show about Anne wanting to go home and you can't just remove that without changing the entire show, which was my point.
The method of travel is just a symptom of the divide in the style of storytelling. People die in Eastern stories because the show isn't about Earth. It's not about the character wanting to go home, so they 'die' as a way to cut off that connection immediately. Instead, the protagonist is used as a way to explore the world around them and its politics naturally. If Amphibia was following Eastern trope conventions, then even with the music box, Anne wouldn't be seeking to go home. She would have settled down with the Plantars permanently while Sasha plots to takeover the world until Andrias pressures her into charging the box; probably as part of a way to 'defeat' Sasha, her rival.