I believe it is mostly folklore that heavier gauge cables are a must.
But I do believe that heavier gauge cables can potentially help compensate for possible design flaws, inefficiencies, and/or simply added for increased marketing hype.
And of course the garden hose thickness always gives the consumer the impression they are getting their monies worth. There's that WoW! factor there that is impressive every time my mother-in-law saw my old thick cables.
I know you are asking about power cables. But if you look at say the Audience Au24, Audio Tekne, or Nordost Valhalla speaker cables, you will notice that these cables buck the traditional heavy gauge speaker cable trend that we have been told must be present for proper sonics.
The Audience Au24 speaker cables are no thicker than my keyboard cable connected to my computer. And the Au24's are the best I've heard, especially in the bass and mid-bass regions. Simply an awesome cable at a reasonable price.
I believe the same holds true for power cables. To a point anyway, heavier gauge simply helps convince the buyer that they are buying a product of substance(even if they are not).
Please don't get me wrong though. I'm sure there are plenty of excellent power cables mfg'ered with heavy gauge cabling. I just don't think it's an absolute necessity as some would have us believe.
-IMO