Summoner and Bard abilities do not chain into each other.
Monk does not work the way you describe either, each skill you use after does not always do more damage than the previous, and works with stance changes, not combos. BLM does not either.
Only Dragoon works that way.
I do agree that jobs can be repetitive, since you usually use the same abilities when playing a certain job, and that does not change per fight, but each job does play differently from one another.
Scholar and WHM do play differently as well.