Inspired by Chiang, I think tree graphs as taxonomies can massively accelerate how quickly people can absorb concepts. As a notation, it allows for breadth-first understanding of linked ideas and the 'whys', instead of patching together bits of depth-first competence. I've played with them for introducing complex topics and people are shocked at being able to absorb things that took others years to apprehend. The knowledge is not competence, just as the map is not the territory, but exploring territory with a map is very efficient.
My own interest in representing concepts led me to my current project where, I found that the poor quality of security assessments was more an artifact of how we represent systems and risk, and not the knowledge of the person doing it.
Like Wolfram, Chiang's story, and others in the OPs list, or even the Luther Bible, a translation from Greek and Latin to regional German, notation can have the same effect as automation, and the challenge of a new notation is that it disrupts the equilibrium in the economy of people who were gatekeepers to the previous one.
In this way, notations aren't just a detail, I'd say they are technologies themselves. It's such an important area.