Hi DJ (?),
Your example in post no. 15 (top right quadrant, labeled "sample shot noise") is a misleading presentation of shot-noise. What you are actually displaying is a large number of pixels/samples, each and every one from Poisson distributed random noise. Each pixel is the product of a different level of signal, hence it has different mean levels with an accompanying probability distribution at each spatial sampling position. You are not showing "sample shot noise", but you are showing multiple samples (one sample at each pixel position). A better label would have been "many shot noise samples", but it would still not show the nature of Poisson (shot) noise, which was the topic.
I respectfully beg to disagree. The issue is that a real image is an example of non-stationary Poisson noise process - i.e., in theory, the noise statistics are different at each pixel location, which you yourself noted, hence, the top right image does indeed show a single sample sequence of such non-stationary noise, and as I mentioned in the post you referenced, derived using the top left image as the "true" signal.
You also do not mention the fact that the human visual system will notice noise more when the signal levels are spatially more uniform. In parts of the image where the signal spatially fluctuates rapidly, IOW lots of detail, the character of the noise is much harder to appreciate and often less of an issue.
The way I see is that how to develop a simple model of noise vis-a-vis signal even in such signal fluctuation cases, which is btw what happens in a real image, so that we can move forward to questions such as snr at image level, the effect of resampling on that snr, best possible window sizes in spatial averaging, frequency analysis of non-stationary noise, and all sort of other interesting questions.