Do good power cords have to be stiff?

The Shunyata power cords I use are very stiff, the Acrolink  power cord is very flexible.

May I ask which Acrolink. I have 7N-PC9700 and 8N-PC8100 and both are very stiff.

Based on my limited experience with different power cords, the stiff and heavy ones sound better than the flexible and light ones

I am using Furutech cables made by VH Audio with 12 gauge S-032N wire and they are fairly flexible also not total garden hoses. And they sound good.

I have made PCs with Oyaide Tunami V2 bulk cable that sound good but are quite stiff.

I have also made PCs from NOS Western Electric 10ga wire, both in 10ga and 7 ga configurations that sound good and are reasonably flexible too.  The NOS Western Electric 10ga wire is also used by TWL in their American 10 and 7 PCs, and was used by previously by Mojo Audio in their well-regarded PCs. The stuff makes nice speaker cables too.

I've gone mostly to DIY power cords which are quite unwieldy but, back in the day, I found the offerings from Wolff and 6Sons Audio to be both very good and quite flexible.  6Sons Audio Golden Eagle is the best power cord I've heard.  Neither come up very often but usually are a bargain at used prices.

Good power cables are often solid core and hence stiff by nature: to wit: Nordost, Acoustic Revive et al…