I went back to read "The Curve of Least Energy" by B.K.P. Horn more carefully. He writes: "Unfortunately, the Cornu spiral is not optimal either...".
In this web page, prof. Albert K. Harris explains the Elastica curve: "If you compress a long thin metal rod, when it eventually kinks its shape will approximate one of the elastica. This is said to optimize the spatial distribution of bending stress..."
And finally, in "Non-linear Beam Analysis" Japaneese aircraft structures engineer Toshimi Taki uses Elastica curves to generate something very interesting:
This is the first time I've seen anything similar to my own diagram of bending curves. I'm really excited!
Maybe the Cornu Spiral isn't the answer to 2d-bending after all?