The only reason marking chords in a tune works is because the principal notes of that tune at that point form that chord. This is what I mean by arpeggiation, not a solid chord of many notes played as one, but the same notes played in a sequence, not necessary ascending or descending linearly. Arpeggiation does not have to be rapid, like a gliss, it can be picking out each note individually, and in any order.
In fact, it works the other way, the notes of the tune dictating what the chords are, and because the notes will rarely define a full chord, it allows some scope for different chords in the same place, as the chord, in adding notes not in the tune, puts a variable colour on the section. Are notes a third apart the base of a root chord, the top of a first inversion or the middle of a second inversion? Three possible chords off just 2 notes. And that's just from the 3-chord trick: if you're playing sevenths you get four for your money.
Try it with a tune you know, changing one chord where the tune behind it's a bit weak into another which shares the same two notes in the melody. It can take the tune somewhere radically different, most likely "wrong", but sometimes only subtly so.