It turns out that using black point compensation for the display does give very different results, depending on the actual monitor profile being used. This is what I found to be so surprising - I sort of thought that results of using or not using BPC would depend only on the monitor profile’s actual black point, assuming of course that one is using a monitor profile that results from using good profiling software that actually provides an accurate monitor profile black point (this is what I get from “assuming what happens” instead of “experimenting to see what really happens” 
). But in reality it also seems to to depend on the rate and angle at which the monitor profile xicclu curve approaches the x-axis. This “rate and angle” in turn depends on the type of profile that you make, and also on what your monitor is capable of displaying after it’s profiled, which in turn depends on the monitor’s native capabilities including its native “gamma” and black point.
I put together a test image that allows to show the difference your monitor profile makes, and also the difference between using and not using black point compensation with different monitor profiles:
For this test image, on pixls I can’t see any squares until reaching the next to the last row. In GIMP-2.9, if I use sRGB as my monitor profile, I can see a lot more squares than I can if I’m using an actual monitor profile made using ArgyllCMS or DisplayCAL. And the darkest square I can see depends very much on which monitor profile is being used, and also on whether I’m using BPC.
GIMP-2.9 allows to freely experiment with different display profiles and settings. But of course the image can be used in any imaging software including web browsers. The strange thing about Chrome is that on my system there are fewer visible squares than with Firefox, which is expected given that the shadows seem crushed more on Chrome. But also the Chrome the visible squares have a warm reddish hue instead of neutral gray like they look in Firefox. The warm hue isn’t noticeable unless I immediately switch to Firefox to look at the same image.
How many squares you might see also depends on how bright the ambient light is (in darker rooms, more squares are visible) and on how dark the surround around the image is,: to see the maximum number of squares make the surround black and the room completely dark. How many squares you can see also depends on your field of view, ohow close to the monitor you happen to be, how well your eyes have acclimated to the light level, and how well they are shielded from glare, and I’m guessing also on how bright the monitor is. Try making the room dark and even using a “viewing tube” to focus in on only one square at a time, not that this even remotely resembles how we actually view images on the web.
As an aside, at one point Firefox 4 did support black point compensation, but that was back when Firefox used LCMS as the CMS. You’d think that if they decided to use their own in-house color management, at least by now they’d have added support for all four rendering intents, it’s been many years since they dropped LCMS.