A journalist asked the same question. This was Steve Sells’ excellent answer:
"The pre-amp output is pseudo balanced i.e. balanced impedance. Great for long runs (for example, to active loudspeakers) and cancels noise pick up. The headphones are actually single ended. There’s only a stereo amplifier driving them. The advantage of the 4 pin XLR and Pentaconn is not to have a balanced connection but to have a 4 wire connection. This connection allows for a separate ground for Left and Right channel. On a 3 pin headphone socket the ground connection for L&R is shared. This shared connection degrades the sound.
Having a true balanced drive would not affect the headphones themselves. Headphones are just a coil in a magnetic field. It doesn’t matter if one end of the headphone coil goes negative and the other end goes positive or if one end stays at ground and the other end moves 2x as far. There will be no pick up like long runs of interconnect cable.
Having balanced headphone amplifiers (or bridged) could in some circumstances sound worse. Not because of the headphone but because now there’ a more complex amplifier driving the headphone. A balanced amplifier will cancel its low order even harmonic distortions such as 2nd. It will then add the odd ordered harmonics such as 3rd. The cancellation of 2nd psychoacoustically exposes the increased 3rd. The 3rd may sound a bit more forward and fatiguing. Each half of a bridged headphone amp effectively sees half the impedance compared to a single ended amp for the same impedance headphone. This again increases 3rd harmonic. Best to keep the harmonics low order. 2nd harmonic is barely audible."