In fact, I think it is more simple in LCH than HSV/HSL.
Let’s put it this way: HSV/HSL is a color representation, not a colorspace, and an HSV triplet does not correspond to an unique color (exactly like an RGB triplet does not define an unique color, unless you also specify the color space like sRGB, AdobeRGB, ProPhoto…). Hence, the same saturation value corresponds to different visual saturations depending on the RGB colorspace from which the HSV values have been derived.
Moreover, the HSV representation is not perceptually uniform, and therefore the visual saturation does not stay constant when you scan the H values at fixed S.
On the other hand, the CIELCh colorspace has been designed to be perceptually uniform, and to approximate a constant visual saturation for a given C value across different Hue values.
Coming back to your original question, the fact that the three sRGB primaries have different C values is simply a consequence of the fact that the blue sRGB primary is closer to the spectral locus than the red and green ones (as can be seen here), and therefore a “pure” sRGB blue is “visually more saturated” than a “pure” red or green. This statement is probably not 100% correct from the mathematical point of view, but should give you the idea…
The bottom line: CIELCh is a better representation than HSV/HSL if you want to edit colors in an intuitive and device-independent way. For example, you can fix C and change h in order to make colors warmer or cooler without affecting the resulting “perceived saturation”.
By the way, RawTherapee has LCH curves to play with, and I have a few LCh-based editing tools in the coding pipeline for PhotoFlow…
Hope this helps!