I tune by ear and have never used a strobotuner or any other electronic device. I start with a tuning fork, and then tune everything else by ear—counting the beats in the overtones to determine the best frequency for each note. I have heard the arguments in favor of electronic tuning, but in my experience the final result is a less pleasant sound.
A machine only “hears” one overtone. You can set it to tune octaves, twelfths or whatever. However, it is still listening to just one harmonic relationship. When I tune by ear, for each note I start with the octave and then check the fourth, the fifth and the tenth. For the high treble and the low bass, I check double octaves as well. So my positioning of each note is much more sophisticated than any machine could ever accomplish.
There is also a question of aesthetics. In some areas of the piano (especially on spinets) the overtones are very distorted. You have to decide whether it sounds better to tune to the octave, the fourth, the fifth, or some compromise in between. This is an aesthetic judgment—a judgment about what sounds best. A machine cannot make aesthetic judgments.
Give me a call and hear the difference for yourself: