Do good power cords have to be stiff?

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…

Just look at some of the Puritan videos on youtube.  The epitome of flexibility, combined with great performance.

Cardas power cords (lower level, which I what I know) seem flexible compared to most (as do lower level Nordost, though I haven’t handled those myself0