The act of working the lather in with the brush means that the brush hairs get under hair to be shaved and lift it up ready for cutting, as well as softening the skin and loosening/exfoliating dead cells as you say, which would add to the exfoliating effect of the razor. The time taken working the lather in also gives time for the hairs to soften as well. So it really is a much better way to shave than using a cartridge..!

That does also support my hypothesis that the blades are really poor steel! But remember, safety first..! I hope you didnt hurt yourself too badly? I always find that cuts from a razor bleed like stink! Must be the ultra fine edges. I sliced my thumb with my DOVO Black Star when I was cleaning it, and it took half a roll of loo paper plus a gallon of superglue to stop that one.