Bigram = phoneme theory (language agnostic)

[Emma May Smith]

Jim Reeds did an experiment along these lines of thought in the 1990's.
One could take the most frequent bigram, and consider that this bigram is really meant to be a single character that has been written out with two symbols.
One could then replace them all, and repeat the process for the next most frequent pair.
One could do this repeatedly in the hope to 'normalise' the entire distribution of pairs.

While I don't think he showed the details, he did say that it did not lead anywhere.

While I understand the point of your whole post, I struggle to translate the entropy value to how the glyphs work. I respect the number are correct but I guess I don't really have a "feel" for them. This is my failing, not the concept of entropy.

I do wonder what the successive stages of Jim Reeds' experiment would look like in terms of entropy. Or even something simpler focussing on the most restrictive glyph. If you just deleted every example of q at the start of a word followed by o. What would the outcome be?