It’s funnyI suspected the same. My uneducated guess would be that feeding the pedal a flats-through-neck-pickup signal results in drive that is happening, just not audible. The somewhat weak upper harmonics and strong low end push the pedal, but while a roundwound string would ring out with much more treble content to fetch the distortion, the flats gets zilch.
I described the exact above to the alpha omicron when played finger style with coated strings… and that was with active pickups set 50/50 neck and bridge.
I never originally like the B3k as it was how you describe but when I had my other overdrive too “crunchy” for me / I setup the B3k in almost opposite off the normal videos and darkglass sound - I have it as an always on but if exciter for my low strings - bass full on, blend mostly clean and the top end mostly cut. So no clank, sounds like my normal bass sound except a bit of growl on my B and E strings if I dig in.
I usually use that for half my band stuff, or individually an mbd1, green Russian muff clone or the Justin chancellor fuzz wah (with the B3k on to give it a bit more wall of sound)