I don't know if folks will find this interesting, but here is an example of something that came up recently in another thread. If you apply a simple curves adjustment in the software with which I am familiar, you increase contrast in the three color channels and therefore increase saturation as well as contrast. Sometimes you might want that, but sometimes you might want to keep the two adjustments separate. I haven't examined other related adjustments, such as a levels adjustment, but I think it would behave the same.
First, the original, washed out, foggy image:
Now, the fairly extreme curves adjustment:
Now, the effect of applying this curves adjustment with a normal blending mode (photoshop):
And last, the same curves adjustment set to luminosity blend mode:
The point is not whether one of these is superior. This is just an illustration of the difference between applying a contrast adjustment in the normal mode and applying it only to luminosity. I believe that you would get the same thing as the last image if you switched to LAB mode and set the curves adjustment to the "lightness" channel, but I didn't test that.