A chord in our context is a symbol in the sheet music, by which the players are told which notes to play for accompaniment and which scale to use for any improvised melody. Thus the "passing notes" may follow the chord.

In other words: Chords are practical in some styles of music that include improvisation, or as a shorthand notation for guitarists, accordionists etc.

Harmonic analysis of, say, a Beethoven string quartet is quite a different matter.