I have long been convinced that the reason the piano occasioned such a burst of compositional genius was that it revealed as no other single instrument ever had (with the possible exception of the viola d'amore) how the ear works.
Having learned to interact with the natural horn, exploring Beethoven's Op. 17 sonata for natural horn and piano, I am more convinced of this than ever.
It is a matter of sensitivity to the coexistence of natural overtones with unnatural mixtures of unpredictable clashes and blends for, because of its mechanics, the acoustics of the piano was always about that coexistence--from day one, regardless of the temperament to which it is/was tuned.
A not-so-funny affirmation of this is that pianists, young and old, professional and not, often attempt to mask the unnatural aspects of its sound by always playing with soft pedal and with the lid down. I did it for years so I know what that is all about.