Yesterday I had two excellent reasons for using theoretical categories warily: one was the first movement of Beethoven's "Moonlight" Sonata, the other the Allegro innocente movement of a well-known Haydn Sonata in G.
Looking first at the Beethoven with a theoretical eye, one sees a triad repeated four times in the right hand over a whole note in the bass. Listening to the piano, however, one hears an unfolding of overtones releasing a wealth of sonority far richer than a triad. This is especially true if the twelve units of the four triplets are grouped in fours rather than threes. Try it: you will be amazed at how much more interesting (and difficult!) the piece becomes.
As for the Haydn: I asked the young student to identify the most frequently sounding tone in the first four bars. The answer, not G but B. Played with B in the foreground transforms everything in the movement. All of the wit of this clearly humorous movement is revealed as turning on that unlikely tone. Try that, also.
Brilliant composers for the piano rarely used static harmonies because the instrument comes alive in its overtones. Trust it.