Good question.
A class d headphone amp design would be perfect for low/no heat and low power draw portable HP amps. Moreover, if the physical size scales well, the thing could be very tiny. Even smaller than the current altoids and more powerful and more efficient, with longer battery life.
In fact, I would bet this could be the only practical amp design to use in a fully active headphone. One in which the amp was directly wired to the transducer within the can itself, and optimized for that transducer, similar to active speaker designs.Implemented properly, with SOTA materials, it could be the ultimate HP.
Imagine a HP amp adequately powered by a watch battery or two that lasts for a month or more.