I think it’s a neat idea. I’ve responded to a few other commenters with my thoughts too, so check the thread.

Would this more intricate engineering result in a noticeably better product for the average guitarist? Would it just be a niche curiosity for audiophiles and engineers?

This is AskSCIENCE so it’s not surprising that you would approach the musings from this perspective.

But OPs idea is about the intersection of science and art. I think the question is really: Would some of these ideas result in an output signal that was controllable in a new way?

Imo this modification would empower an artist to interact with their guitar in a novel and creative way? Do I think we’ll see mass adoption, no, but I think there are definitely people out there that would be interested in playing a guitar with pickups like this. Even if it’s just part of their creative process.

I think OP is interested in the role of oscillation planes because with an acoustic guitar, exciting a string parallel (lateral) to the guitar vs perpendicular to the guitar has a perceptible difference in tone.

OP believes that this difference isn’t captured by common electric guitar pickups.

From what I’ve read in this thread common pickups measure the speed of the string, basically considering both planes of vibration the same. But an acoustic guitar responds more to the perpendicular oscillations than the lateral oscillations. (Because the perpendicular plane oscillations tends to work the bridge/soundboard, and push air towards and away from the sound hole).

Although I agree that ultimately the string’s oscillation is pretty much circular/cylindrical/bi-conical, but I suspect there is a significant transient effect that could be explored/exploited with redesigned pickups.

I’m also curious if it would be possible to use a string with a [section of] non-circular cross section to allow the [creation and] detection of torsional vibrations.