Good one!
Balanced headphone out has disadvantages;
- two amplifiers will have twice the noise, twice the distortion and twice the output impedance.
But in a battery operated device where max. voltage swing is limited by the battery's voltage, using balanced, we can use the same battery twice (using two amps) to get twice the voltage swing (i.e. 4X power).
It is merely a trick to get more power out! if the extra power is needed, the above is a small price to pay.
However, there are devices that use 2X "DAC/Amp on a chip" (such as Fiio BTR5). On such devices, using SE uses much less battery juice, because the second chip, as a whole gets switched off, but it would sound better on balanced, perhaps because some of the distortion components cancel out, because identical DACs are used against each other. (A theory)