This public post by Eric on the ColorSync user list in 2008 might be useful (I find any post by Eric has some useful information):
Yes, but what is described there seems like overkill for most users. As a photographer, we generally don't want to *correct* the on-scene lighting conditions, instead we want to capture the mood of the on-scene lighting.
If I am in a forest with a lot of green light surrounding me, I generally want to preserve the green light, not completely correct it out of the image. Or if I capture a sunset scene, I generally want to preserve the warm colors dominating the atmosphere. While it would be useful to know the character of the light so I can correct it, perhaps just partially, we already know that that can be done quite adequately using tri-color profiles, and mostly very basic whitebalance tricks like a graycard or a white plastic lenscap/cup .
And the sunset example would be my preferred example to show that dual-illuminant profiles are merely a convenience, and may be confusing the actual capture process: i.e. we want to capture the atmosphere of a low temp scene by selecting the normal daylight response and only correcting the graybalance partially.
Whether this "normal daylight" response + graybalance correction is adequate under most circumstances, even tungsten, is indeed an interesting question. IIRC Magne Nilssen was the original creator of the capture one profiles, and he used to mention something to that effect in posts at the time.