This may be true in some set-ups, but the reality is that not all SE designs are created equal and sometimes the balanced output is cleaner on the amplifier. Whether the headphone is balanced isn't necessarily going to be the deciding factor, a balanced amplifier circuit may or may not sound better than a comparable SE circuit. On my Aune M1S, balanced sounds better, and with cans that need more juice, balanced will almost always sound better than the SE output on the same device simply because balanced outputs more power.
I fully intend to test whether the X5iii's balanced circuit sounds better than the SE at volume matched levels. In my experience this isn't always the case and an SE output on one unit may sound better than the balanced output on another unit, but you have to have a balanced setup to know this and identical cables. With the UERR I have their stock cable and their balanced cable, both have identical construction, so this makes a very good control. It is also a headphone that is sensitive to small differences in sound quality, so will be good for the test. I'm looking forward to doing it.
In the meantime,
@HaPeKa shouldn't worry about going and getting a balanced headphone setup, as it very well may not make a difference.