When I embed a color profile in a jpg image, I give you the option to see it just as I had created it. If you don’t, I will never see your image as you had envisioned it. This post explains why embedding color profiles is important, how can you even get to see color profiles, and how can you test if your browser actually reads them (i.e., is color managed).
I describe here the make of a photograph, with deeper thoughts in mind. If a photograph is just a representation of reality, then what would it be if we change it in some major way, say, by erasing all colors? Is it still a photograph? If this is an artistic decision, what is art?