The usual sensor uses basically three types of element -- R, G and B
-- in a particular layout.
Why not X Y Z where X = R+G, Y = R+G+B, Z = G+B ?

You can get RGB from XYZ easily enough:

  Y-X = R+G+B - R+G = B
  Y-Z = R+G+B - B+G = R

  X+Z-Y = R+G + B+G - R+G+B = R

But the total light you are accepting is 2+2+3 = 7 rather than
1+1+1=3, so you are getting more photons overall. Isn't that
beneficial?

Y also gives you a straightforward monochrome.

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