Every screen and printer will display/print colors differently. This is not a good idea.
If the colors are quantized into a constellation, even significant error could be corrected.
But I’m sure you too feel that the failure modes of this colored barcode form a proper subset of the failure modes of its monochromatic counterpart.
The primary problem I see is that so many industrial cameras today are black and white. B&W cameras can send at a higher framerate and you don't need to convert to greyscale as your first step in your algorithm, so it saves time to use b&w cameras.