Wrong way round.
ah, okay, I've confused that. Sorry.
Problem here is what I've mentioned above.
Paper white in paper profiles is often blueish/grayish - at least if the profiles are measured by devices without UV cut filter.
This is due to optical brighteners in papers (not all papers of course, but most photographic papers contain optical brighteners).
But blueish white is not white. It is not only bluer than white it's at the time darker than white.
But your Paper is visually … white.
What happens with your softproof if use paper simulation?
I've taken the profile a FUJI paper (RGB printer / C-print) because these papers contain a lot of optical brighteners so the problem is quite obvious.
This is crop from a sky with clouds - screenshot of the original file:
[attachment=17097:01_sp_off.jpg]
This is the file with softproof relative colormetric + BPC / simulation of black ink:
[attachment=17098:02_sp_rcm_black.jpg]
This is the file with softproof relative colormetric + BPC / paper simulation.
Due to the relative colorimetric RI you can see quite well the blueish white of the paper - and it's darker.
[attachment=17099:03_sp_rcm_paper.jpg]
This is the file with softproof absolute colorimetric / simulation of black ink.
Color management spins the blueish paper white to the warmer white point of the display.
(too, the contrast range is compressed to the level of the paper contrast but is displayed at the luminance level of the monitor - so no compenstion).
[attachment=17100:04_sp_acm_black.jpg]
This is the file with softproof absolute colorimetric / paper simulation:
[attachment=17101:05_sp_acm_paper.jpg]
In the last screenshot the white point compensation works fine so far but where are the transitions of the clouds?
They are suppressed on the monitor preview - but they are visible in the print (as in screenshot #2).
The blueish (and therefore darker) white (which is nothing else than a measurement device error) compresses the transitions in bright tonal values.
You'll find the same effects of compression all over the tonal range of the image… just less obvious in less bright tones.
This effect is clearly visible with papers containing a high amount of optical brighteners and less visible in papers with a small amount of optical brighteners - but still there.
This is why it is not a bad idea to calibrate the monitor to paper white (both luminance and white point) and set the softproof to relative colorimetric RI + BPC (or perceptual RI) and simulation of black ink only - the monitor white already matches paper white so there's no reason to adapt white points for the preview.