Don has already provided an extensive answer - I'll just round it off by saying that the mains power needs to be as "perfect" as possible: zero distortion, zero impedance, zero noise riding on it is the ideal - and how you get that is the roads to Rome answer. Why is this needed? Because the powers supplies and filtering in most components are not good enough, and all the "defects" of the mains are adding to the low level noise/distortion soup in the final sound. Feed any reasonable playback rig absolutely pristine mains, and you're that much closer to optimum sound.
Sorry to be so late on this.
Given The Way Things Work, I would say rather that the component's power supply should as perfect as possible, including isolating it from whatever the mains (incoming AC lines) are doing. Based on my somewhat limited experience over many years with systems from audio to RF I think depending upon the incoming AC power to be clean is folly. With a halfway decent power supply, it doesn't need to be, and isolation cross the power supply is very, very good in the vast majority of components, at least the ones I have seen. Then it is up to the designer to provide adequate filtering and decoupling on the output side of the power supply to feed the electronics inside. Note filtering may include physical bulkheads and shields as well, and proper layout (of ground pours, power pours, and component orientation) is critical if you really want extremely low noise. Not that most audio components really need go to that extreme for the noise to be inaudible. Again IME/IMO.
Cost also enters into things, natch. Decoupling on the boards my company designs is extensive (yes, partly my design, for the HS analog stuff) and thus costly, but results in about 80 dB noise floor relative to the (1 V) power rail. A lot of the cost is due to very wideband (GHz+) decoupling that is not needed for audio circuits; if I limit myself to say 1 MHz then the noise floor is ~120 dB or better. Then add power supply rejection (PSRR) of the circuits themselves, which in the audio band can be another 80 - 120 dB, and it's hard to see power supply noise being much of a factor. IME, while some products due exhibit low-level hum (typically 120 Hz and multiples from a diode bridge of a linear supply), most of the noise is regular old Johnson (thermal), shot, and very LF noise (flicker, popcorn, etc.) generated within the circuits themselves rather than coupled from the power supply (let alone the AC mains).
What I have seen be more problematic is bad grounding; I wish every component had a nice heft chassis ground connection so I could ground them all appropriately and so as to limit any dependence upon the incoming power ground. Can be a challenge, alas, given things like cable and satellite TV feeds that bring in their own grounds, but those can be easily isolated so a nice star or other competent ground scheme can be implemented.
Finally,
@fas42 may have made significant improvement in his old HT system, but to me that speaks to the poor quality of the power supply (probably due to cost constraints), not the quality of the AC line.
FWIWFM - Don