The big problem with this is it would take more bandwidth for us to transmit images.
Using RGB color, you’d do something like #dddd88 or the bits 110111011101110110001000 to send a light yellow. White is #ffffff, or 111111111111111111111111. (3 colors, 8 bits each, 24 bits.)
If instead of that you had “red-green-blue-yellow-white” color, light yellow might be something like #000000ff44 (yellow plus some white to lighten it up) and the bits would be 0000000000000000000000001111111101000100. (5 colors, 8 bits each, 40 bits now.)
White, in this system, would be #00000000ff which would again require 40 bits.
We’d be using more bits, which means either more time or more parallel wires, to produce a color that we could make in the RGB system anyway. Video processing would either go a bit slower, or cost a bit more because of the added hardware requirements. Not sure that’s worth it.
If you really want to make monitors better – check this.
https://upload.wikimedia.org/wikipedia/commons/thumb/6/60/CIE1931xy_CIERGB.svg/325px-CIE1931xy_CIERGB.svg.png
The colors inside that triangle are the ones we can make using RGB combinations; the ones outside the triangle, we can’t hit accurately. (That is, that image isn’t showing them accurately either.) So there are some colors in the pink-violet area that an extra pixel could help us access, and there’s a whole bunch of action in the cyan/turqoise area that we’re missing out on.
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