Bayer filter: why have RGB and not CMY?

We all know the familiar Bayer array: each pixel has either a red, a green, or a blue filter over it so it captures only a narrow band of wavelengths. Blue is approximately 350-500nm, green is 500-600, and red is 600-700. The problem is that each pixel throws away ~2/3 of the light by filtering out the other colors. My question is, why not use a different set, CMY, so that each site captures more light?  It seems to me that the camera could be one stop more sensitive by using 350-600 for cyan, 500-700 for yellow, and a combined 350-500 and 600-700 for magenta, while still capturing the same color information.

It looks like a few early digital cameras used a similar CFA back around 2000 but none since.

Thoughts? Why don't we see this on cameras today?