BPC is baked into the Canon Pro-10 profiles. It's also baked into the Canon 9500 II profiles and my Epson 9800 as well. As a result, the only thing selecting BPC can possibly do add more BPC and this would lighten shadows further. Fortunately, PS and LR seem to recognize that it is already baked in and don't do additional BPC. At least PS CC 2017. Note that the link refers to the aging PS CS6.
The canned, Canon Pro10, Pro9500 II, and Epson 9800 profiles, are not conforming ICC profiles, but in different ways. All three, wrongly, do in-profile BPC in both the Perceptual and Relative Intents. This is perfectly fine and allowed for Perceptual intent since nearly anything is allowed in Perceptual Intent. However, it should not be done in the profiles by Relative Intent. When vendors do BPC in their Relative Intent profiles it makes the profiles unusable for Absolute Intent rendering as they share the same tables. The ICC recognized that some vendors had implemented Relative Intent incorrectly and clarified how it is supposed to be done (it's a pure, colorimetric process scaled only to the media white point) in the last Version 2 spec. and this has been carried over to Version 4.
Profile Maker 5 and the subsequent, I1Profiler generate correct profiles.
BPC, as currently implemented in Photoshop CC 2017, appears to handle these well leaving the profile's BPC unchanged. I have seen no observable affect of BPC on the canned Epson and Canon profiles in any rendering intent. OTOH, I1Profiler profiles. being ICC compliant, do not implement BPC in Relative Intent and so Photoshop BPC is necessary using an ICC compliant profile if a continuous response is desired in dark shadows. If visible areas of an image do not descend below the paper's black point, then a better print will result from deselecting BPC. Otherwise rather ugly blocking and even color shifts can occur on out of gamut colors near black.
My guess is that Epson and Canon implemented BPC in Relative intent to avoid this ugly effect if RC w/o BPC was used. The benefits of BPC are such that most encourage people to always use BPC. Epson and Canon leave no choice to the detriment of accurate Absolute Intent rendering. Likely a market force related decision. Few use Absolute Intent compared to the potentially more numerous group that might print using Relative Colorimetric w/o BPC and don't understand the implications.
Relative Intent, when the requested color is within gamut, should print that color, relative only to the white point. When it is outside the gamut, Like requesting a L=2 very dark black, it should print the closest color that the printer is capable of and it should report back via the reverse tables the L value of the actual color that will be printed. That's around 7 for the paper and setting types shown in the attached graphs.
The attached chart shows the L tone curves of 1 I1Profiler 9500II custom profile (Costco), 2 Canon canned profiles (9500II and Pro-10), and 1 Epson canned profile (9800). Both Perceptual (Blue lines) and Relative (Orange lines) tone curves are shown for each profile. All are neutral grays from black to white. The requested L* is shown on the X axis. The value of L* returned from the profile round trip is the Y axis.
Only the I1Profiler shows the correct responses. The L value on Relative Intent clips when the requested color is below L=8 as seen by the plateaued orange line in the upper left chart. Note how the Perceptual intent show closely matching values all the way from L=0 to L=100.
It's also interesting that Epson and Canon roundtrip Relative Intent differently. Canon, at least, is properly reporting printed L levels. Epson has the curious property that a requested color printed with RI at L=0 is reported to actually print L=0. This is true even with their matte profiles that have a black point over L=20! Totally hosed.