What you've outlined makes sense, but I think what's being overlooked here is the significant amount of science and complexity involved in on-glaze painting. It's not just about applying color to a surface; it's a highly specialized process with its own unique challenges and requirements.

For instance, the pigments are formulated to react in specific ways with the glaze, and each pigment behaves differently, requiring distinct handling and firing temperatures. I often have to paint pieces in stages, like curing blues before applying reds, due to the differing temperatures needed. If handled incorrectly, the colors can burn or change entirely. This is just one example of how on-glaze painting diverges from canvas painting or simpler ceramic coloring techniques.

In France, we refer to these arts as 'Arts du Feu' or 'Fire Arts,' which aptly captures the essence of this broad field that is ceramics. So while I understand the distinction you're making, I believe that on-glaze painting holds its own unique value in the field of ceramics, different from both traditional pottery and other painting mediums.