Rowuk, I love your points in your locked post and yes many times people have referred to notes like this but many times and most of my life trumpet players have refered to it not necessarily from a C centric point of view, but rather you had middle g, what some call 2nd line g, then g above the staff was high g, then the g above was double g. and the one above double high c was triple g. A g below the staff was low g, and then you got down to pedal g, then double pedal g.
When people would say a low A, everyone knew they meant the A below the staff. When they said a middle A, they knew they meant the A in the staff. When people said a high A, they knew they meant the A above the staff and when people said a double A they knew they meant the A above high C.
I agree sometimes people do refer to these notes differently, no doubt about it.
Intellectually I can understand your points.
I am just telling you I have heard it more commonly refered to in this manner for a lot of years. Usually f or g above high c is where I would hear the double expressions begin, then triples at the f or g above double high c.