So I’m more thinking about resolution and dynamic range at this level of abstraction. It is not a question of new sound, but more like texture for various modes like palm muting, clarity, adjustability, or natural/pinch harmonics. Most effects are basically modes of bad audio in amusing ways from clipping to poor recording delays, or what it sounds like to play audio through junk materials like plates or springs. Pursuing perfection is nonsense for sure; pursuing resolution and nuances might yield new and unique sounds.
I forget if it was Veritasium, Steve Mould or one of the other edutainment content creators that was showing how waves move through a string and form the extra major harmonics along the length. I was half baked thinking of that and how the string is not constrained to a single plane of vibrations.
I am thinking of the motion of the string being more complex, like if I placed a coil under the string and one at 90° to the first beside the string, there should be a subtle difference between the two signals. The motion of the string may be oscillating entirely within the field of each pickup coil, but the motion with respect to the magnetic pole of the pickup will be different. If two fields are pointed at the string from opposing angles, perhaps more of this motion is defined. It might alter the sound for more subtle picking techniques like plucking, slapping, palm muting or others.
Also there is the question of what is the optimal turns ratio and signal for each string. If each string had its own pickup and winding, it is like audio channels on a mixer, it creates versatility and nuance. It’s just an idea.