OK, I've spent a few minutes to do ultra quick tests with what I had at disposal. All pics show the crude (intentionally not "normalized") response of humbuckers when excited through an ultra low impedance air coil, with volume full up then lowered. Vertical steps of 3dB.
Below is the hi-gain ceramic HB evoked in my previous post. As already mentioned, it has a single pot: its volume control. The low capacitance of its wiring promotes the sparkle when its volume is lowered (pink line).
Now, here is a mid gain HB with a LP style wiring (toggle switch far from the pots), necessarily more capacitive since there are more and longer wires. Although the tone pot is not enabled (being a no-load control) and leaves active the 500k volume pot only, the higher capacitance of the whole wiring contributes to dampen the sparkle, even if the resonant peak is still higher pitched when the volume is lowered...
NOTE - This pickup is covered. A part of the sparkle is dampened by the related Eddy currents.
Below is the same pickup than above but with no-load tone pot enabled AND lowered - it's connected in the 50s wiring fashion, BTW... See how the volume now controls a much wider range once lowered, giving a clearer tone, while a part of the lost sparkle gets back (black line in this screenshot, to compare with the pink line above)...
Finally, here is the response of a hi-gain pickup with a crude 1nF treble bleed cap on its volume control (still no tone control in this case)... Unlike 50s wiring, the treble bleed cap tightens the bass range. Works very well with this precise HB. Might sound a bit thin with another HB, which would then require a resistor in series or in parallel with the cap...
Hope it illustrates that pickups don't really clean up efficiently or not by themselves* or at least, not alone. Their performances largely depend on a whole system : a same humbucker might clean up in a magnificent way with 50s wiring in a SG and become very muddy sounding with modern wiring in a LP once the volume lowered, because of the parasitic capacitance of the wiring harness (among other factors)...
*NOTE about the pickups by themselves: As I've tried to explain it several times in similar topics, the capacitance of their coils and cables / wires before the volume control is still critical. That's why many hand wound coils tend to clean up in a more transparent way than machine wound equivalents. But there are not many artisans able to hand wind humbucker without loosing the higher Q factor of "classic" (machine wound) PU's and the related voicing with it....
FWIW.