I think I explained it pretty well in the video. I'm not sure that "Most people who would buy this device are audio enthusiasts". If anything, I reckon that the opposite is more likely to be true at this price point. What I found when doing reviews is that a lot of people were watching them ended up confused, because they weren't audio enthusiasts and didn't understand even simple things about a product -- knowledge we take for granted with our experience. It's easy to forget that we're part of a very tiny corner of the internet.
The balanced output has more power, so at least with full-sized headphones, the stronger amplification might make a noticeable difference. However the possibility of simply it being louder, resulting in a better perception of the music is very likely true as well.
For those that haven't watched it, I said in my video was that I wish that FiiO had made instead a single-ended output that was as powerful as the balanced output is. It is quite possible to make a high-quality SE output. I believe the misunderstanding amongst enthusiasts is that balanced is better in general rather than better in an individual product. For example, is the balanced output of the BTR5 going to best the SE output of the M11 Pro, just because it is a balanced connection? Obviously not. That way, a consumer who just wants to buy the BTR5 to use with whatever regular headphones or IEMs they have, doesn't get the shock upon buying the product that they have to spend more money to get the most out of it.
