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The thing to realize about ICC profiles in the workflow is that they are for soft proofing.
The way profile based management works, the printer profile what guides the conversion of your file's RGB values to the gamut of the printer when it is printed at WHCC . The results are limited by the physical properties of the ink and paper, mechanical variables, etc. It is what it is.
In absolute terms of measurement of color a print NEVER matches a screen 100%. But if you've seen wireframes of color spaces in 3D like this comparison of my iMac and the printer next to it...
The significant thing to take away conceptually is that the part in the center where all gamuts over lap — about 80% of all gamuts — do match. The colors hanging out that don't match, in theory, are the most saturated colors.
If you photograph a topless blond in a day-glow lime green bikini bottom draped across the hood of a red Ferrari the colors on screen or print will not be an exact match, but if everything is in calibration you'll get a perceptual impression that you are looking at the real thing on screen and print. Why? because most of the gamuts of the scene you see by eye and on screen and print are common the all the gamuts. The only thing that shift around are the extreme colors like the red in the car and the green of the bikini the screen and print can't match. But you will be too busy looking at the blonde's boobs to even notice.
The point being that the ability of the brain to adapt perception is why we think a print matches screen to the extend we do. That's where the printer profile used for soft proofing fits into the workflow...
Heres a photo...
Here it is viewed with soft proofing with the HP printer profile shown in the gamut comparison with the "out of gamut" (OGW) warning engaged.
What does that tell me? Which colors I can expect to be less saturated on the print. With the "out of gamut" warning off it looks like this on screen...
I got similar results in the screen shot above by leaving the OGW on then manually reducing the saturation.
Nothing I can do in PP an make the printer print a deeper purple. That is limited by its cyan and magenta pigments. But I can do things like change contrast a bit to make it seem like the purple is more saturated.
The viewer of the print, if they never compare the print with the monitor, will never notice the purple isn't as intense and in terms of overall message it doesn't matter. What matters in how the person in the foreground looks. Go back and look at the shot with the OGW and the saturation correction. She wasn't out of gamut on screen or printer and her appearance didn't change much when the printer profile used to "filter" the file> screen image.
For the most part what causes changes from scene capture in camera > print are saturated colors in the scene the printer's ink can't match. The Ferrari in the print won't match the car if laid on the hood if the printer can't do Ferrari red. The screen can't either, but it can by virtue of having red pixels create a brighter red than the print. So relative to each other if monitor and print are put on the hood, neither match but the screen is more accurate. So if you use the printer profile for soft proofing its more of a warning where to look for changes on the print, not a way to prevent them.
If you were to buy a Ferrari and picking the color Ferrari wouldn't send you a printed brochure the would send you paint clips of the same paint as on the car because that's the only way to see the true color: stand in the empty driveway with paint chip in hand an imagine its the Ferrari glowing red in the sun.
In the same way if you are making a really critical large print the best way to evaluate how I will print is to print a small section of it on the same print before starting to edit. The put the file in soft proof mode and compare the actual test print with soft proof. If they aren't a good match then it tells you not to trust the soft proof to predict actual results. If test print and soft proof using printer profile are a good match then you can edit in soft proof mode to try to improve the file. If you leave the OWG warning on it will tell you when a correction you make in the file has pushed saturation beyond what the printer can deliver.