It strikes me just like a phono input the guitar input was designed more for cost than for best performance. Since a pickup is a coil it is natuarally balanced. If lower noise is a worthy goal then run the signal down twisted pair into a steup transformer then into the amp input. I bet you knock 20-40dB from the noisefloor.
Most of the noise in a guitar pickup is due to EM interference picked up by the coil itself, so in order to reduce noise you would need to use a pair of differential coils with opposing magnetic fields (aka a Humbucking Pickup). You wouldn't gain anything by using a balanced output itself.
I built a Bass Guitar and incorporated a DI transformer and XLR output into the design, I powered the internal electronics from the phantom supply, too!
It wasn't any quieter than the normal 1/4" "unbalanced" output.
Les Paul's personal guitar (for a time) used low impedance pickups (~600Ω) because he observed that all of the telephone equipment and all of his recording gear operated with a 600Ω impedance.
He did that for "fidelity" reasons, however, not noise. Gibson finally offered that setup in their Les Paul Recording Model Guitar in the 1970s
It featured a "low-z" output and a hi-z output , via a step up transformer for use with a normal guitar amp: