A SIMPLE ILLUSTRATION, that luminance in an image is more important than color:
This shows the colors from an image, stripped of its luminance.
What is in this picture?
Of course! They are ducks!
The fact that human vision includes color ought to strongly suggest that color is important; but it is also known that human beings can thrive without color vision, as do many animals, and so it isn't of great life-and-death importance — icing on the cake, perhaps.
The color-only image, taken from the a* and b* channels in Lab mode in Photoshop, looks at best excessively abstract, and at worst silly. The monochrome image is rather mundane, but quite recognizable without color. Certainly, there are many images where color is far more important than this example, but clearly color alone is not particularly useful — or beautiful — if taken to this extreme. The color-only image file is smaller than the luminance file, which, according to information theory, tells us that there is likely less stuff in the file, less information, suggesting that color is less important.
Many fine photographers state that having an excellent black-and-white version of a photograph is an important step in creating an excellent final color image. When working with an image, ask yourself these questions: Do you have good detail in both the highlights and shadows? Do you have good local and global contrast? Does your image look good without color? Is color something added to make the image look even better, or does color cover a multitude of sins? Color is important, but is less important than luminance.
I generally use the Dan Marguils method of using Photoshop, as described in his book, Professional Photoshop: The Classic Guide to Color Correction (5th Edition). However, he notes the trend of advanced Photoshop users adjusting color and luminance separately. But we do have to be careful, since luminance greatly effects color in the highlights and deep shadows. For this reason, I typically use the Gamut Warning feature in Photoshop to make sure I'm not losing significant detail.
Occasionally a young commenter on the Digital Photography Review website will question the importance of black-and-white photography; often, these critics will consider that technique old-fashioned, or merely a by-product of obsolete film technology, something that is best forgotten and never reproduced in the future. But even the latest digital cameras can do monochrome images quite well, and as I hope I showed above, it is more important than color.