I didn't mention them since they have nothing to do with synthetic vs natural dyes though -- they're properties of whatever materials the dyes become part of.
That's actually a significant part of why "accurately" photographing clothing for online shopping is so hard. Getting an accurate hue is usually fairly easy with good lighting and proper white balance, and gray cards let you calibrate brightness. But the reflective properties of fibers mean that e.g. a shirt can look significantly different depending on what angle the light sources are at.
I guess that is what I'm getting at, that today's conception of what a "dye" is, is that it is a substance which is added to a material not changing the reflective, translucent etc properties of that material (which is itself probably a simplification - I can't imagine dying a fabric doesn't change these at least a little bit).
What I'm suggesting as an advancement is perhaps not called a "dye", but nevertheless would be a new way to not only change the color of the target object, but also the translucence, iridescence, reflectivity, etc.
I know there is already stuff in this area - there was some laptop case I saw recently that had some kind of micro-texture on it (the opposite of a polish, I guess) in order to make the black color of it more matte (if I recall correctly). Likewise, anti-reflective coatings and privacy screens seem like a ubiquitous, primitive example of what I'm talking about. I'm sure there are others.
Seems like a great technological opportunity for someone to figure out.
Recently I advised someone not to buy granite countertops sight unseen, since the way they look in person is so different from the way they look in a photo - a photo completely misses the reflections, iridescence and other three-dimensional aspects of the actual product.