I work with signal lines in shipboard engine rooms daily. Lots of rotating machinery, high RFI/EMI/"Noise" environment. Not Apples to Apples but close enough. Shielded cables are a must in that environment. The shields "pick-up" all the interference before it gets to the conductors and "shunts" it to ground so it does not reach the equipment interior.
Out of curiousity, are these cables shielded to the power source or just from a junction box to a device (machinery)? Ideally, I'd think one would have shielded Romex or similar on runs to outlets used for audio equipment. BX cables, other armored wire, or wiring run in metallic conduit should help here, I'd think. I'll have to research this a bit more.
Actually in a system shielding is important for all your cables, it is in fact how noise can get into the system. I don't expect someone with a receiver, one turntable, and a CDP with a pair of speakers to need anything special. However in my system with separates, many front end components and power amps I can use all the protection I can get with cables crossing each other.
And as I said, I had a problem with some AC power cords when slipping in new to me power amps. They where mono blocks that i ran the power over other cables to test in my system. hummmmmm, swapped the amps leaving the cords, hummmmm stayed on the same side. Started to mess with the speaker cables on that side, that wasn't it. The next morning I stared to unplug stuff to do a better install, thats when I found the power cords where not the same. I replaced it with what looked to be better and no hum. It's no secret to keep power cables away from everything else or even the the preamp, thats why they make multi box preamps. Dirty box clean box, the dirty box has your AC and switches and is the controller for the clean box that has all the preamp in/outputs.
Basically, if I understand correctly, you had noise (hum) issues in your amps that were created by your audio system (not a criticism, just wondering). I'm curious as to why the amps' power supplies weren't filtering this out. I take it the 'noisy power cables' were still of good quality. I wonder if there was a problem with the ground or something.
It reminds me of issues I had with some Cat5e cables I was using on HDMI extenders years ago. All was good until the freezer, washing machine, or HVAC system switched on. All sorts of problems popped up then, eventually leading to a loss of signal or handshake issues. Moving the Cat5e away from the power lines stopped the interference, but that meant I had to lay them on the ground of the crawlspace - not a good thing. Switching to Cat6 resolved all these issues.
What I'm getting from all these posts is that audio systems can cause enough interference to be clearly audible. In such cases, higher quality shielded power cables can help. Following best practices by ensuring cables of different types (AC, speaker, line-level, etc) are not run parallel to each other and being mindful of their spacing, along with good quality cables, can also solve and prevent such issues. For systems that don't have these issues, such measures are likely to not be audible, assuming the cables are of good quality (in terms of gauge), plugs and receptacles fit tightly, and low level cables and connectors are properly shielded and fit tightly.