It's a good question. I touch on it a little in my thesis (mostly chapter 2). First, there is psychology literature from the 50's [1] that indicates that curvature minima and maxima are salient, so having superfluous curvature extrema makes a curve less aesthetically pleasing. Hobby splines suffer from this, if you arrange the control points in a zigzag to make a serpentine, it places curvature extrema just on either side of the control point.

Second, there's all the log-aesthetic stuff from Japan, [2] has links to a lot of papers. Honestly, I find their claims of aesthetic beauty to be fluffy, not backed up by hard empirical evidence. I did do a small amount of human evaluation research in [3], which suggests that the log-aesthetic curves are visually pleasing, but the math for their use in an interpolating spline (which is the subject of TFA) is less stable than Hobby splines, Euler spiral splines, or Minimum Energy Curves (all of which are fairly similar).

I think there's more that could be done here. Thanks for your question.

[1]: Fred Attneave. Some informational aspects of visual perception. Psychological Review, 61(3):183–193, 1954.

[2]: https://www.yoshida-lab.net/english/research-e/log-aesthetic...

[3]: https://levien.com/phd/LevienSequinCAD09_014.pdf