What
@Roy G. Biv said. Plus: Complexity.
A fully balanced (as in: differential, aka "proper and not fake") amp requires about twice the amplification circuitry. Which means more parts, more space, more heat, bigger transformer — considerably more expensive.
Where a balanced signal shines is in signal integrity, because it inherently cancels out noise introduced into the signal while it travels through the interconnects.
With headphone amps, the impact of that benefit is arguably small, since you tend to have really short interconnects between your gear. Short interconnects means a considerably smaller noise impact from potential RF sources.
Balanced interconnects make the most sense in speaker setups, especially if you place your power amp as close as possible to the speaker with longer interconnects and short speaker cables (which is the recommended way), instead of close to your preamp with short interconnects and long speaker cables (which works fine, but is not quite as ideal).
Note that balanced headphone connectors are a whole different story altogether. While those are being called "balanced," they're not the same thing. Balanced interconnect signals are two separate signals per channel, 180º out of phase to another, for a total of four signals transmitted through eight wires for a stereo setup. A balanced headphone signal is one signal per channel, for a total of two signals transmitted through four wires for a stereo setup.
So why do these "balanced" headphone cables exist? Because they allow for the separation of ground. A single-ended headphone cable has three wires in it, a positive signal per channel each, and a single ground wire shared by both channels. Giving each channel its own ground
can (but not necessarily has to) offer slight advantages in channel separation, it helps keeping crosstalk at a minimum. How noticeable that benefit can be mostly depends on the overall quietness and quality of the amp, and how good your ears really are. An argument can be made that a little bit of crosstalk can actually enhance your overall stereo image, especially with older recordings where mixes often have a much stronger channel separation than is customary today. In some cases entire instruments are limited to just one channel (see the main title track on the soundtrack for the movie Charade for a particularly extreme but not exactly rare example). Too stark a separation sounds unnatural, especially with headphones, because your brain is used to always hearing the same sounds through both ears.
Long story short:
For headphone amps, truly balanced doesn't necessarily make as much sense as it does for speaker setups. The relatively small benefits you get from a truly and fully balanced chain in a headphone setup is not necessarily worth the added complexity and cost that doing so would entail.
