I tend to agree with you that there is no valid scientific explanation re: much of the wire claims. That said:
1. Several sub assemblies (e.g., transformers and most digital products) spit out a lot of noise that can, indeed, travel back through the mains. (Bringing up the need for isolation at the plug, which is a different topic)
2. Quality insulation helps the noise from going somewhere unwanted.
3. A lot of supplied power cords do skimp on copper gauge and nice fitting plugs. Electricity and interference will take the path of least resistance. So a low (by which I mean bigger) gauge wire provides an easier path. I’m not opposed to the idea of a high gauge wire might be starving a component for a bit, either.
4. Nice wires tend to be bought longer and are more flexible. So people take more care with routing of interconnects and mains so they cross at 90 degrees and don’t run close parallel, which also helps with interference.
5. Tight fitting plugs make a better connection. Hence why hospitals use hospital plugs.
Note nothing here discusses magic crystal wire with unicorn hair.
Just low AWG wire, with good copper, nicely insulated (say, the kind the IT guy buys for your company router) and perhaps a secondary sheath, of generous length for proper routing, with hospital plugs. Not cheap stuff, at all.
Different, but related, issue: components need space and isolation. They all generate all sorts of noise. The interactions are so complex it might as well be voodoo.
Source: I was an electronics countermeasures officer in the very first Gulf War hunting SCUDs in the middle of Iraq from a POS Kiawa helicopter with no weapons packed with finicky electronics.