Yep I believe most school house want *first* to emphasize to young pilots the conceptual difference between non precision approaches (2D Apps) and precision approaches, where for ages everybody did the same way, ie dive to the MDA and maintain it until the missed approach point. The schools don't want pilots to confuse between approach types and may teach [the traditional] different techniques to make the pilot behavior help differentiate APPs types. I would bet it's a pedagogical approach rather than a complete course an all the developing stories on how to fly an approach with CDFA to MDA + addendum.
Then later in the airlines, and depending on SOP and budget, the CDFA may be seen as a supplementary technique to teach in order to bring commonalty of operation for all approach types, but the aware pilot still is able to discern between the various approach categories.
Maybe just reassure them that you have perfectly understood the underlayin concept... and nevertheless will apply CDFA techniques.
Also, in accordance with the evolution of flying techniques, private providers and State chart depictions may differ for the same approaches.
Approach_minimums_LIDO_Jeppesen.pdf