yes, it's confusing, but it's correct.
You have to think laterally here (I always forget about that as well): the softproof simulates a certain output (paper) profile. Now this paper profile is displayed WITH BPC to the monitor if "simulation" is deselected. I.e. the paper contrast range is displayed within the contrast range of the monitor - not within the contrast range of the paper itself. So from paper to monitor there is a BPC.
With "black ink" selected the (paper-) image is displayed without BPC on the monitor... i.e. without stretching the paper-contrast ratio to that of the monitor.
With "black ink" selected you actually have a relative colormetric view of the paper on the monitor.
So in short: "black ink" is boosting the black point of the display to that of the paper. The result is that you are viewing the contrast range of the paper itself not that of the monitor.
I use "black ink" all the time, I never use "paper simulation" (see above).
I don't want the DR of the monitor when I am trying to simulate the DR of the paper in a soft proof. Checking "Simulate Paper white" does this for me.
To keep this discussion dead-easy and grounded in reality - and my experience with thousands of prints using differnet papers over the years:
- to get as close a matching as possible between the display and my Epson 3800 output with Photoshop Managing Color, The Customize Proof Condition needs to have both BPC and SPC checked using RelCol or Saturation RI.
- with Perceptual RI BPC doesn't matter, but SPC does.
- with AbsCol RI BPC is greyed out, but SPC matters.
- under all RI, Simulate Black Ink is checked and greyed. All my images leave LR or ACR with ProPhoto RGB embedded.
(Preserve RGB Numbers is always unchecked).
Getting back to the OP's issue, I think Andrew Rodney's post (#5) is likely the most relevant factor and relates directly to the question I put to the OP about what "all the way down" means for his display. But the OP should get back to us on this.