Even painting would be completely incapable of producing realistic "colors," and we'd all just have to agree than the ochre blob really looks like a rose.
You could still mix the paint to be the color of a rose, since the rose's color is also just a pigment. Worst case, you get an actual rose and try to find some way to stabilize the pigments. We might have developed sophisticated organic chemistry at an earlier stage, simply so we could produce art. More likely, the artist's palette would simply have a lot more colors on it. Mixing would take more time and skill. Paintings would be more expensive. High-end painting was always for the wealthy anyway though, so I don't think art would have been hurt too badly. If mixing colors was too difficult, then the worst case is that art might have been dominated by grey scale techniques for a long period of time.
The task of developing a decent computer monitor sounds harder. Even then though, there would be some binning of frequencies. How much spectral resolution do you need to appreciate music? If I can barely tell the difference between C and C#, I will never be a great musician... but I might still be able to appreciate it on some level. If each pixel had 16 different frequencies and 16 levels, it would obviously not look real to people with high spectral resolution. OTOH, it would probably look better than monochrome. It might be like listening to a scratchy old AM radio--better than nothing.
I think color representation would be like 3D: a fad that comes and goes but never quite sticks because it is so hard to do and because it can never be right.
Color paintings would be mostly highly abstract with a few rare and remarkable specimens painstaking created over many years. Most realistic art would gray scale.
Photography would be almost entirely black and white.
Computer monitors might well have color but, without effective mixing, could only display the actual color present in the phosphors. CGA would be state of the art color.