John,
Thanks for pushing the envelope in data manipulation options, such as you did with the cdata package. I have enjoyed reading your documentation and articles around the ideas in that package in particular -- I have read them several times in the past as I've tried to build my mental model of data frames, especially in relation to database or data cube models. I haven't had occasion yet to use complex pivots requiring this approach, but I learned a lot reading your articles/vignettes.
One topic that your writing has helped/spurred me to think about is the difference between index columns versus measure columns, which I think is an area for potential innovation in how calculations are commonly done in R. The various invariant dataframe representations you describe also seem to have potential representations as n-dimensional arrays or matrices, with named indices. It makes me wonder whether, for example, it would be possible to use S3/vctrs tools to abstract the particular rows/columns combos as an implementation detail for coordinatized data.
thanks,
Jameel