the sound of the interconnect won't be a thingMalarkey!
Assuming balanced circuitry and connections are properly implemented, which far too often they are not, they can reduce common mode noise. FULL STOP.
For balanced interconnects to be immune to cable, they would have to be immune to the laws of physics. Balanced lines [and connectors] have impedance and impedance controls frequency response.
differential amps tend to be lower noise we don't need as much gain stages to get the job doneIf number of stages is a criteria, use a transformer. Differential amps per se are all over the map in terms of gain vs noise. The devil is in the details.
the other reason for balanced lines is elimination of ground loop noiseI'll wager that 6 9's of 'balanced' home audiophile systems do not lift the shield at the destination. Depending on amplifier design, there may be ZERO ground loop improvement over an unbalanced system.
The balanced line system was created to get rid of interconnect cable colorationsThe balanced line system was invented by the telephone company to increase noise immunity and power transfer over long distances. Nominally 600Ω, but at 1 frequency ONLY! Low frequency performance is abysmal.The 'telephone sound' is a direct result of balanced cables.