If you connect earth to "cold" at the amp end, you have not got balanced line operation, and you do not get hum cancellation.

Hum cancellation occurs when the "phase" signal and "antiphase" signal are added at the transformer or summing amplifier and because they are added out of phase with each other interference signals cancel each other out.

Humbucking guitar pickups do use this effect, creating two out of phase signals by having the magnet pairs of reversed polarity and therefore two signals of different phase that can be added not subtracted (ie added out of phase with each other). This is what makes playing with the wiring of the little switches that can be used to make a humbucking pair into (1) parallel humbuckers (2) series humbuckers (3) North single phase (4) South single phase (5) Additive single phase and (5) out of phase. It is real brainache stuff to figure out which three versions you want and how to wire the funny special DPDT switches used for the purpose to get the combinations you need. I Always have to go and look it up and compare several disagreeing cribsheets to get the answer and if you have a south/south or north/north humbucking pair instead of a south/north pair it is a nightmare!

Oh, also some high end acoustic guitars with internal preamps do have a mini-XLR output, so presumably do run a balanced output.