Nice trick. Won't work for measuring the sky, though.
For representing all colours: if you have a set of three LEDs the spectrum of which perfectly match the sensitivity of the colour receptors in the human eye, then you should be able to recreate all colours humans can distinguish.
First problem: men and women have quite different colour perception. Women can distinguish many more shades in the green/blue/purple parts of the spectrum. That's even before individual differences (which is more than just colour blindness).