Yes, some ICC profiles show results we did not expect. BPC in ICC, M2/M3 measurements...
I check a "normal" ICC generated by caldera RIP (M0 measurement), it uses x-rite's color management core. Under CIED tag, there are all measurement spectrums. I calculated black target readings and averaged, get L* = 4.240. Other methods list below:
PS 2-step convert: 5
PS convert and curve-tool finding 8 bit value: 4.706 (12/255)
ICC bkpt tag: 4.146
ICC A2B1 tag: 4.249
ICC viewer (iccview website or ProfileMaker's Gamut View) can only provide a guess around 4~5.
Using a regulars ICC profile, the A2B1 tag has closest value.