Very cool idea, Sandpiper.
I found an IEEE paper from Kodak employees that talks about this. Here's the first paragraph of the intro. (I assume this would be considered fair use. Feel free to delete if you think it's not, mods.)

Single chip color CCD image sensors sample the scene
using a color filter array (CFA) integrated on the surface of
the sensor. In these sensors a given photosite samples only a
single color. A variety of CFA patterns can be used, with
various arrangements of red, green, and blue (RGB) or of
cyan, magenta, yellow, and white (CMYW) colors.

This paper is from 1989, and since it's so old it seems to me like there must be some reason besides manufacturing inertia why this hasn't replaced RGB bayer arrays. Does anyone have any ideas why this wouldn't work as well?

The only thing I can come up with is that it would be more difficult to go from counted photoelectrons back to photons. For example, in the magenta photosites blue and red will pass the filter and blue light will create more electrons per photon than the red light will. This would cause issues with white balancing, but it should be possible to get the information back with a (just slightly) more complicated interpolation algorithm. Maybe processors weren't up to the challenge back then. As for me, I'd like to see that extra stop!

I was reading a link I found somewhere about a possible new CMYK sensor. But my wife had to use the computer "right now", and when she was done, she had sent the link to oblivion. :( I will try and recount what I can remember of the info before I was interrupted.

As I understand it, the new sensor design has several advantages. First, rather than use the narrow filters of an RGB sensors, the CMYK sensor uses wider color filters. IE, Y is R+G, so the Y sensor utilizes the spectrum of both R and G light. Same for M = R+B, and so on. So inherently each sensor site has available twice the light spectrum from which to gather light, resulting in a two fold increase in light, ie. 1 f-stop. So as I understood it, the sensor inherently is 1 f-stop better than an RGB sensor.

Second, it captures the data in the CMYK color space that is needed for printing, so fewer color space changes are needed in processing.

The last advantage, that I did not understand very well, is that the use of the fourth sensor also gives a slight increase in sensitivity and resolution because it is a forth channel that can be used in processing. Apparently the K sensors are quite small, and do not detract appreciably from the space utilized by the C, M, and Y sensors. As I read it, the K (black) sensors can be quite small, as their function in life is to capture black, and it does not take a large sensor to "get almost nothing".

Sorry I have lost the link, but that's one of the liabilities of being married! Maybe someone can find it again and fill us in with more detail.