I certainly cannot add to the explanation given as it is exceptionally comprehensive. My personal experience, as limited as it likely is compared to many others on the forum, is that the additional power and lack of noise on the balanced set up I use was something I could not find in a single ended system at the time of purchase.
I picked up a Little Dot MK-VII+ amp when they were still stocked by LD and paired it with a silver balanced cable for the Senn 650s. As much of a skeptic and bargain hunter as I was, I couldn’t deny that the balanced connection provided a punch and clarity at higher volumes which had been missing with other SS amps I had tried near the same price point.
A year or two after I bought the VII+ I was going to recommend it to someone but when I spoke to LD (David Zhezhe?) I was told that the cost to manufacture them had become too much to build them on spec. He said they could special order it (at the time) but that the cost would be significantly more than what I had paid.
I’m sure there are likely single ended amps now that sound as good or better for the price but I’m afraid I became somewhat biased towards a balanced set up. Perhaps it’s largely due to the lack of interference and/or ground loop problems from the source to the amp as well.
As far as I can remember this application is mentioned as an advantage, even in the article you referenced but it’s a long time since I read the Benchmark write up (I may read it again if only to check my facts 
)
Even after this long I don’t feel much need to upgrade the amp but my DAC could certainly be improved on.
A tube amp has been a big a temptation (as are top tier cans) but I’m afraid I might end up in the poor house if I start up searching for audio nirvana again! I’m still happy with what I hear from this old gear but always keep my eyes and ears open.