I was thinking, you know how in the GCN game if you don't save while in somebody else's town, your face becomes that of a Gyroid? well, I realized, Coco's face looks almost identical to the player's when they reset in another person's town!
Since Coco has been around since the GCN, perhaps she was once an Ordinary Rabbit, who forgot to save in a town she visited, and thus Lost her face for the rest of the games to come? The Villagers obviously know about, and presumably save. And KK Dirge playing if you give her a Music Player adds on to this whole thing!
TL;DR Coco forgot to save while visiting another town in GCN
Since Coco has been around since the GCN, perhaps she was once an Ordinary Rabbit, who forgot to save in a town she visited, and thus Lost her face for the rest of the games to come? The Villagers obviously know about, and presumably save. And KK Dirge playing if you give her a Music Player adds on to this whole thing!
TL;DR Coco forgot to save while visiting another town in GCN