Cleaning up dirty power is the job of the power conditioner, the job of a good cable is to not decrease the quality of the power (signal) and prevent other nearby cables from getting noise from it.
With a perfect amplifier, or a perfect power conditioner, it should not matter, but previous tests at least in my system show that it does matter quite a lot.
Do you know the three things we often talk about for speaker cables: resistance, inductance, and capacitance? They all matter for power cables as well.