Do good power cords have to be stiff?

The Shunyata power cords I use are very stiff, the Acrolink  power cord is very flexible.  I also have 3 of the 7 gauge Pangea power cords which are almost impossible to bend. It’s is weird that these Pangea cords work well with my speakers where their 14 gauge ones sucked the life out of the system. 

most are but some aren’t

i use some excellent homebrew braided 3 conductor pc's that are uber flexible by a friend in the midwest - pm me if you are interested

Signal Cable.

Verastarr or other flat or ribbon cables for the win! Many round cables are so overly wrapped and shielded that they are practically unusable and surprisingly cover up generic readily available cable. Never buy without a right of return. 

@tom6897 excellent point- many years ago I had a pricey balanced cable that was poorly terminated to the point that one leg broke off. I undid the Neutric connector, pulled back the tech flex, pulled back the company's own cable cover only to find that it was Belden cable. Nothing wrong with Belden, but it was a belden cable all dressed up.