Put another way, there are the following possibilities and ensuing questions:
1 - the problem is insoluble.
Q: what's the best practical solution that we have now, and are there any obvious ways to improve upon it
2 - the problem is soluble, but has not been solved.
Q: Again, what's the best practical solution currently available, and what would be required to improve this solution to the point that it meets the challenge
3 - the problem is soluble, and has been solved
Q: Is this solution commercially available, and if so, practical for individuals to implement.
As long as cameras don't meet the Luther-Ives condition, the problem is not perfectly solvable. However, we can come pretty close, for limited lighting spectra and limited subject matter. For those, the problem is close to solvable, given a camera with a tractable set of color filter array dyes and an appropriate lighting source. A demonstration of this is the success of heritage preservation photographers in color reproduction. The key to successfully doing this is using patches of the materials to be photographed, illuminated by light that is the same as will be used for the actual photography. Gather the patches, measure them with a spectrophotometer, photograph them, input the spectra to the profile making software along with the raw file.
The problem can also be nearly solved, and more accurately, by using a monochrome sensor and a filter wheel consisting of more than three segments. But there is no nonspecialist commercial software to deal with such a camera. As the number of segments in the filter wheel increases, the accuracy of the solution improves.
But most photographers don't want accurate color. Hunt defines possible objectives for color reproduction:
Spectral color reproduction, in which the reproduction, on a pixel-by-pixel basis, contains the same spectral power distributions or reflectance spectra as the original.
Exact color reproduction, in which the reproduction has the same chromaticities and luminances as those of the original.
Colorimetric color reproduction, in which the reproduced image has the same chromaticities as the original, and luminances proportional to those of the original.
Equivalent color reproduction, in which the image values are corrected so that the image appears the same as the original, even though the reproduction is viewed in different conditions than was the original.
Corresponding color reproduction, in which the constraints of equivalent color reproduction are relaxed to allow differing absolute illumination levels between the original and the reproduction; the criterion becomes that the reproduction looks the same as the original would have had it been illuminated at the absolute level at which the reproduction is viewed.
Preferred color reproduction, in which reproduced colors differ from the original colors in order to give a more pleasing result.
Most photographers want the last. That gives a lot of wiggle room, although it introduces an element of subjectivity. All the commercial raw developers are set up to attempt to deliver the last by default, and there are huge controversies about how well they do that, with hotly-debated opinions on all sides.
I see this is getting long. To be continued.
Jim