That was my original intent. However, when I stare at it and visualize it with color, I'm concerned that the color will lighten it up and change the dynamic of the sprocket.I do understand the "it's only original once" thought but I think it would be cool if the black out area is painted the same color as the bike. Besides it would look cool and be unique for your daughter to set her bike apart that much more.
It's a tough decision, which is why I haven't made it yet.