I just read through an old (2012) thread that describes this issue in great depthA "typical" PC LCD monitor has a contrast ratio 1000:1. With a gamma of 2.2, the left pattern 6,6,6 is below the black level, and right pattern 15,15,15 is barely above the black level.
Thus, it's not really the "fault" of the calbration software. Specifying black-point compensation during calibration will help.
in particular, post #172 sums it up:
Most of the PC Monitor calibration software uses 2.2 gamma as the default target; coupled with the low contrast (1000:1) and high ambient light level, the end result is severe black clipping.Following the power law curve exactly as far "down" the curve as we can adjust, will ensure that at some point (~4.6% Stimulus on my set @ 2.2 gamma) near blacks will simply merge with black (aka clipping.) IOW, if we follow standard practice for setting black level, but neglect to apply at least a linear offset black level compensation to our power law EOTF, we haven't really solved anything.