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I'm currently reading Color Design Workbook: A Real World Guide to Using Color in Graphic Design, but it's a bit short on color theory basics. I was wondering: in CMYK, black is added to the three subtractive primary colors to improve the rendering of blacks, which would otherwise be brownish. This addition of a fourth pigment increases the gamuth of available color.

So, my question is: has there been any serious proposal to add a fourth primary to the additive RGB colors? One can imagine that this would allow for more vibrant non-primary colors, for example in the “violet” region, in high-end display devices. One obvious downside would be the price of such new technology, and I know it is not widely available, but: has it been considered?

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Yes, it's been considered and manufactured. One such technology is the Quattron display technology from Sharp. This technology uses a fourth yellow sub-pixel which "increases the range of displayable colors, and which may mimic more closely the way the brain processes color information".

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As @mspasov points out, the yellow range has been the color of choice in wide gamut experiments. It's just not enough for people to shell out the cash. Pantone did the same in print with their Hexachrome palette (adding orange and green to CMYK). Fantastic colors but very few want to pay for the extra plates. There have been a few notable exceptions in the case of Hexachrome, Odwalla juice packaging being one of them. –  plainclothes Nov 16 '12 at 6:20
    
@plainclothes: also, many inkjet printers, even for home use add light cyan and light magenta –  e100 Nov 16 '12 at 10:05
    
But variations of the same hue aren't doing much to extend the spectrum, it just makes subtle refinements. –  plainclothes Nov 18 '12 at 5:24
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Since the cones in your eyes have their greatest sensitivities to red, green, and blue, those three colors should be sufficient to display any color. It is not a problem with the number of primary colors, but the range. For example a typical computer display has 256 levels of each color, the display is limited to a little over 16 million colors. If you want more vibrant colors, then increase the number of discrete steps, not the number of primaries.

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While it's not quite what you are asking, some phone displays are RGBW, with a 4th white subpixel to give a brighter display at the expense of colour information.

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