Continuing to think about this, there might be another, more likely, reason not to use the 2.5mm balanced output. as a radio antenna, which will probably be valid for all DAPs. As I understand it, one of the main points of using a 2.5mm is to reduce EM interference. The balanced cable carries two copies of each channel's signal. One of those copies is phase shifted before the wire begins, and shifted back before the termination of the wire, where both copies are added, resulting in higher power output which is also desirable in this case. The signal summation after the final phase correction removes all the EM interference received by the wire, and with it FM radio frequencies.
If one of you is an electrical engineer, feel free to chime in and correct my basic idea of what a balanced cable is.
