So this got me thinking. Since a lot of pickups these days are constructed with the two ends of the winding coming out through two conductors of a shielded cable, and one side only gets grounded to the shield at the guitar's output jack. If you replaced that jack with a TRS jack, connected the two ends of the pickup winding to the tip and ring of the jack, and the shield of the pickup cable to the sleeve, you'd have a balanced connection if you connected it to a balanced input with a TRS cable. You'd also have an unbalanced (conventional) input if you connected it with a standard TS guitar cable.
I suspect that most noise is picked up by the pickup rather than the cable, but if that cable does tend to act as an antenna, the balanced output and differential input would improve the common mode noise rejection.
Now, this isn't a construction project yet, but food for thought for those of you who customize the wiring in your guitars. There are obvious considerations about how to deal with pickup switching and controls that need to be dealt with. As a thought exercise, though - a single pickup wired straight to the jack - it seems like a pretty good idea.
I remember back when dinosaurs roamed the earth reading an article about Chet Atkins in which he said he made low impedance pickups for his guitar to get lower noise and less high end loss, but he didn't say specifically that they were balanced or what he was connecting it to. Gibson made a Les Paul Recording model which indeed had low impedance balanced-wired pickups with an XLR connector at the output, and a special amplifier to go along with it. So the idea isn't new, it just, I guess, never really caught on.