I know it's a magical profiler and all, but ...
I love magical things. I had a pair of pickups once handmade by the real Mr Bill Lawrence in the USA, originally Mr Willi Stich from Germany. He put some mojo into it and it sings. Just screams, "Play me! Play me!"
One does not simply look a gift horse in the mouth. There is a point beyond which adding gain to an already distorted signal starts to muddy things up. But that added mud seems to add "girth" to the signal, makes it fatter, seems to make it chug in a thicker voice. Sure there's a lot more hiss and fizz and sputter, but you' ll mainly hear that if you put your ear up to the cone. Standing and playing a little further away, it barely annoys. You might not even notice it.
That girth, or fatness, to the tone could be the bass frequencies that Mr CK is talking about. It's sort of added body to the sound, but not something tangible. It's like mud forming layers, it makes things fatter, but might not be in a symmetric fashion, the layers could be unevenly stacked, or the stones within might not be lining up evenly. Sort of like the grain in a wood -- might be too flat pieces, but the textures could be odd.
They say bookmatched timber is the best for making guitars. Would be interesting to learn more about the Kemper's controls, especially whether it bookmatches the gain
I apologise if this all sounds pseudo-scientific, it's because we are firmly in the realm of philosophy