I think you misunderstand the fundamental difference between "white" LEDs which are generally a blue LED associated with various phosphors that convert the monochromatic blue light into a mostly continuous spectrum going from blue to red, and the monochromatic R, G and B LEDs that each emit a fairly narrow band that is either red (with no blue or green at all) green (no blue or red) or blue (no red or green).
Blue LEDs are used to create white because it's easier to convert blue to lower frequencies. But red and green LEDs absolutely exist. LEDs exist for a wide range of narrow wavelengths, including for example infrared LEDs that emit at 940 nm without a trace of blue (obviously, otherwise they would be visible!).
