One of my professors (a viola player) was fond of saying that G-sharp is not in fact the same pitch as A-flat. Then again, he had the luxury of playing an instrument capable of any possible pitch within its range limitations. (Lack of frets will do that to you)

This, in my mind, brings up an important point in this argument -namely the acoustics of chords and our overtone system. With a string instrument, it is capable of listening for the overtones of a chord to get the sound to "lock in." This is especially evident with a major chord. If you do the first and fifth correctly, a "ghost note" of the third will come out, which is (I believe) slightly lower than what you have in a well-tempered instrument.

Instruments with tone holes, in contrast, are limited by where you place the holes, with various compromises being made based on the limitations of the overtone series used. This, more than the usage of the piano, I imagine would be the reasoning for the creation of a set tuning system. By creating a set pitch for each note in a scale, it then becomes possible for an instrument maker to create a consistent wind instrument. Brass instruments have the same problem, although it involves more being able to place in different size tuning slides than anything else.