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The issue with color to grayscale conversion for human consumption is in most cases there is no well-defined ground truth. People don’t see in grayscale, so the appearance preservation approach doesn’t work. And the source image was most likely heavily color corrected to match certain aesthetic. So the problem becomes “to preserve as much information, both content and aesthetic, within constraints of the target grayscale medium”.

The bottom line is, use some standardized conversion (like described here — just to avoid surprising users) if images don’t actually matter, some contrast-preserving method if content matters, and edit creatively otherwise.

Since this is all perceptual anyways, go ahead and compare some color formats for yourself. I'll say that for me Oklab is the most perceptually accurate at lightness representation