Quote illegal colors:
Now, what I don’t understand (I’m really dumb when it comes to electronics) is how is that superior to simply getting rid of common ground? And if there are advantages why the same principal never used to drive speakers?
It's all rather misleading, and has nothing whatever to do with a common ground (or lack of it).. and the same principle is used to drive speakers, particular in in-car systems using (ground free) bridged amp configurations because of the limited 12V power supply typically found in cars.
The main issue here revolves around this statement:
"This method of driving headphones effectively doubles slew rate and power output, and halves the output impedance of the amp as seen by the headphones".
This is true, but only in comparison with a system comprising the same amp in a single-sided configuration.
It is perfectly possible to build (unbalanced) headphone drivers with as high a slew rate, power output and low impedance. As many of the high end headphone amps demonstrate.
Does it mean I can use DAC1 USB’s balanced outputs to drive 300-Ohm Sennheiser HD650/600/580 headphones?
No, it means theye have included a decently engineered (unbalanced) headphone amp that is capable of driving 300ohm headphones (amongst others) very well via the usual TRS headphone socket.
Can I simply re-terminate a stock HD650 cable replacement for balanced operation?
You could, but there would be no point, and it wouldn't work with many outputs properly.
Technical Editor, Sound On Sound