I once did a fairly long post regarding this, but I think just the four example images will tell the story.
It would have been better if I had something with the blue and the red at the exact same level, but it's a real world image, and is close enough.
IMAGE LINK: https://flic.kr/p/gewFcz
Hunting Percival (BAC) Jet Provost T Mk 5A
by
Alan Evans
, on Flickr
Straight desaturation. The red and the blue are very close in tone.
IMAGE LINK: https://flic.kr/p/gewsFb
Desaturated
by
Alan Evans
, on Flickr
Using a tool that allows colour mixing, first lets make the blue channel very dark, and the red channel very light.
IMAGE LINK: https://flic.kr/p/gewuv4
+Red -Blue
by
Alan Evans
, on Flickr
And now lets reverse it, and make the red dark, and the blue light.
IMAGE LINK: https://flic.kr/p/gewwGs
-Red +Blue
by
Alan Evans
, on Flickr
By being able to manipulate many channels it is usually possible to ensure that you can maintain contrast between different colours, even when the brightnesses are identical. If you simply desaturate then there is no method where you could change the level of one colour compared to another, where the original levels were the same.
Oh generally it is much harder to bring the blue channel up than the red. In colour digital sensors it is usual to need to push the blue signal by a significant amount during the WB process, so then adding even more boost to the blue tends to add a lot of noise very quickly. The blue was quite a bit darker to start with too.
Alan