Note with CCD cameras (not CMOS), in camera binning (as opposed to post binning) reduces the read noise as there is only one dose per binned super-pixel
That is true, but the read noise adds in quadrature whereas the signal adds. The post-binning signal to noise ratio per NxN binned pixel is N times that of the unbinned pixels.
That is why I was careful to state that the dynamic range can be improved by a factor of NxN for N-fold post-binning, and not the signal to noise ratio. Sometimes the dynamic range is particularly important, such as when trying to detect extremely low contrast objects for instance.
FWIW, I generally use in-camera binning for photometry and post-binning for simple detection. The reason for the former is primarily for faster download times and smaller image sizes, rather than any read noise consideration. Read and dark noise is so small on my cooled CCD camera that it is completely overwhelmed by photon noise from the object and the sky. It is way down in the noise, to coin a phrase 😉
Entirely agree about the under/over confusion but failed to mention it earlier. I am pleased that you have done so.