Very well put, and that corelates exactly with my findings. I was able to easily dial the color temp of the LED array to whatever color temp I wanted. And when viewing the source directly, its color was undistinguishable from a high CRI 4100K fluorescent, or incandescent source. But when I used the array to illuminate objects, the colors were off. Skin looked magenta...
Good points. Natural objects do reflect very complex spectrums.
I am not sure that I agree that the situation is as bad as your quick testing may have led you to believe, because by your logic, 3 chip color cameras which use 3 separate CCD's and narrow band dichroic filters would all render totally unacceptable color scenes, but they seem to do an outstanding job in the real world.
The eye has it's own limitations in this regard, due to the the tri-stimulus characteristics of human color vision, so I suspect you could improve things by choosing LED's with optimal center wavelengths and spectral widths.
Did I miss something? Is there some difference between three narrow band LED's bouncing off a surface, vs. a broadband white light source being bounced off the same surface, then narrow band filtered by equivalently narrow band dichroic filters in a 3 chip cameras?
In a pinch you could always use a variation of the CYMK trick used in printing, by including a high color rendering index white LED along with the Red, Blue, and Green chips.
In this configuration, highly saturated colors would be rendered by the R, G, and B drivers alone, and less saturated colors would be mixed with more and more 'white' light from the white LED as the color saturation decreased.
So there would be no compromise, even if the issues you raised do cause problems.