Count me in the perplexed category.
Already assumed after our discussion of gamut and color numbers.
Profiles are always paper specific, not just printer specific.
Both!
If so, it would be logical to expect that, not matter what paper, the resulting image would look the same or very similar, as the profile would/should compensate for any differences.
Logic based on misunderstandings of color management isn't sound logic.
I understand that certain papers can not achieve the same maximum black, but color balance should be another thing. After all, the idea is to match print to screen, and screen is always the same.
Color balance is based on lots of items, one of them the white of the paper and your perception of that white. And yes, the idea IS to match print to screen and why, those of us serious about it use a reference display system that allows us to calibrate to multiple calibrations to do just that. We consider WP, contrast ratio when we do so, we end up with differing calibrations per paper due to that. Do you expect that if you send the same RGB numbers through a good profile to vastly different papers, those papers play no role? If not, how can you assume one target calibration for a display accounts for the differences? It can't.
It's funny to read people all over the web state:
"I've calibrated my display and it doesn't match the print". When you ask them what they used for calibration aim points, they tell you someone suggested 120cd/m2 6500K (or D65 which isn't the same). Yes, they did calibrate the display, they just did it wrong! IF you calibrate your display correctly, you do so to produce a match and the settings will vary, one size doesn't fit all. How can it?