If the CFA is bad, non- orthogonal you lose color precision, and cannot recover it in post.
I think that your reply is over-simplified. It should be easy to specify a filterbank that is orthogonal while still being colorimetric bonkers. I'd expect that any filterbank response that can mimic the desired response through a "well-behaved"*) 3x3 color correction matrix would be a good starting point.
The spectral dimension seems to be highly similar to the spatial dimension in this respect. You might say "if you choose a small aperture, you loose spatial details and cannot recover it in post". Except good sharpening/deconvolution can actually bring back details as long as they are still sufficiently large compared to the noise floor (and the PSF can be estimated).
So the question really is (perhaps)
* "how far from the (colorimetric) ideal spectral sensitivity is the color filter array"
* what does the colorimetric ideal color correction matrix look like
* at what ISO/signal levels can this matrix be applied before the output starts to appear "noisy"
It is my impression that Sony (and the MF guys) tends to prioritize accurate color, while Canon and Nikon prioritize luminance sensitivity.
-h
*)An identity matrix being good, but other forms that does not have large off-diagonal terms might also do.