The piano was always out of tune for two reasons:
- Sympathetic vibration: More pronounced in this instrument than in any other, this would have set off a bewildering array of contradictory overtones regardless of what temperament was used to tune the instrument
- Key leverage: The relatively short black key levers, usually struck at the tip, would have released a more resonant sound than white keys struck at mid-point. This would have made some major triads, D major, A major, E major, clearly dissonant.
Instead, visual analysis took over. The hearing of generations of musicians has been conditioned to death by the reduction of just about everything to triadic functionality. If our hearing is now flawed it is not so much the result of equal temperament as of this stifling pedagogy.
Once having learned Mozart as a composer of tonal harmony on the piano it is wondrously difficult to return to the piano's elemental acoustics as the source of his insights and the inspiration for his many sonatas for piano solo or for piano with accompaniment of the violin -- for that is what those duos are, not the other way around.
I base these observations on my initial shock at encountering Mozart's black keys as a child, on a later shock playing harpsichord for the very first time, and my ultimately clarifying shock when, in my 50's, I returned to intensive solo piano playing and could identify the phenomenon.