I spent all too long 15 or so years ago attempting to create a camera profiling tool using just such a technique. The starting point was a spectrally measured target. For any tristimulus value a camera records there are an infinite number of spectra that can give the pixel reading. If, however, you iterate through enough known colors, the possible camera matching functions converge. I can probably pull up GATF and other presentations I made on the topic if desired.
The profiles I created were colorimetrically accurate to a fault. We used them for product photography under controlled lighting. The problem was that mathematical accuracy did not translate into pleasing visuals. Discontinuities in the profile translated into ugly transitions in images. Franz Herbert at Integrated Color Solutions took a different approach of prioritizing aesthetics over mathematical accuracy. That ended up working far better in the real world.
Cameras just aren't designed for accurate color. Scene referred imaging with perfect L-I imaging response still produces relatively unattractive images. However, for reproduction work this, otherwise unattractive, is highly desired since the goal is to create a side-by-side matching copy.
However, even if a camera's imaging met L-I and "perfect (low dE)" prints could be made there are many reasons those may not match the original.
They could have different surface characteristics such as glossy or semi gloss characteristics that differ from the original. Colorimetric processes only retain accuracy when a print is illuminated at 45 degrees and there is no light from other angles that could reflect off a surface. A matte print w/o OBAs, displayed w/o glass, is impacted the least by this.
But even then a match might not occur unless the copy and original are displayed using D50 or a close spectral equivalent. This is because the reflected colors, simplified to the three CIE variables XYZ only match because the spectral characteristics of the original is not going to be the same. The two may be metameric at D50 (and 45 degrees, no uV, etc) but with a different illuminant metameric error will accrete.
And even with all that the CIE matching functions aren't perfect. Individual humans vary too. Sometimes quite a bit. Mostly this affects how two different people will see an image on two monitors, otherwise profiled identically, but with different backlight spectrums. Esp. CFL v LED. Print metameric error tends to be less as reflective spectra is usually much smoother than the monitor's RGB. It's especially noticeable on the shorter wavelength side from 440 to 500 nm where the "B" can match for one person but be off for another.
Here's a deep dive from a student at RIT about 20 years ago.
http://www.rit-mcsl.org/StudentResearch/mshaw/CMF_Thesis.pdfColorimetry works in a well controlled environment but there's a multitude of factors that can confound.