The same could be said anytime you're trying to purify "garbage" : poor recordings, poor source, bad room. I, too, used to be a skeptic. I was espically skeptical of all cables and even most CD players. most recording travel down a $16 XLR microphone cable somewhere during the recording process. Since that is the weak link, why should I bother using a better cable than that? (rhetorical)
Auditioning interconnects a couple years ago opened my mind to that. And recently contructing several DIY power cables have opened my mind that sometimes, a power cable can make a SMALL difference. Even with the junk in the walls.
Try some. You won't hear differences in all systems. This is like the last 0.00001% tweak of your system. But in some systems you will. Maybe yours isn't tuned that well. Or perhaps your ears aren't? Or perhaps you have the wrong power cord? Generally, if you can't heara difference - you have some other gross inadequacy in you system - that may or may not be due to the romex in the walls.
I would fathom of the increased (or reduced losses ;-) ) of better power_cords/outlets/iec_sockets tend to be a result of the improved grabbing ability of the connections in making a solid connection. "Hospital Grade" stuff in known for that. That's why we use stuff like that. Better connections.
And you're right. After power cords. You'll start playing with power condititioners. Then you'll start replacing outlets (might as well, <$10). Next you'll run a dedicated line, one each, for - analog, amplifers, digital gear. Heheheh.