Sorry but some manufacturers claim that some of their high end headphone amps have balanced output.
If that is a true claim, how could it be provided?
If there are 2 x 2.5 mm TRS outputs, then it is possible (though I have not seen this) that they each be configured either, L or R mono as tip in phase (+),ring inverse phase (-) and sleeve chassis ground. This would be exactly the same configuration as a 2 pro audio mono balanced 1/4" TRS channels, just a smaller connector. All I'm saying is that this is not impossible though it is much more likely that balanced headphone output would be a single 4 pin mini XLR. Even though the standard configuration for such a connector includes 2 common ground pins which would exclude balanced out, it is still possible to produce a variant connection with pin out L+, L-, R+, R-, shell chassis ground.
I am not convinced of these claims. I agree that the concept of balanced headphone gets a bit silly especially with high impedance headphones. However, if true balanced output is in fact provided as claimed and people want to play with this, why the hell not? The decision to spend their own time and money on it is theirs surely.