Why does the third noble truth not include the ten fetters? The Four Noble Truths are defined in the Dhammacakkappavattana Sutta as:


  "The Noble Truth of Suffering (dukkha), monks, is this: Birth is
  suffering, aging is suffering, sickness is suffering, death is
  suffering, association with the unpleasant is suffering, dissociation
  from the pleasant is suffering, not to receive what one desires is
  suffering — in brief the five aggregates subject to grasping are
  suffering.
  
  "The Noble Truth of the Origin (cause) of Suffering is this: It is
  this craving (thirst) which produces re-becoming (rebirth) accompanied
  by passionate greed, and finding fresh delight now here, and now
  there, namely craving for sense pleasure, craving for existence and
  craving for non-existence (self-annihilation).
  
  "The Noble Truth of the Cessation of Suffering is this: It is the
  complete cessation of that very craving, giving it up, relinquishing
  it, liberating oneself from it, and detaching oneself from it.
  
  "The Noble Truth of the Path Leading to the Cessation of Suffering is
  this: It is the Noble Eightfold Path, and nothing else, namely: right
  understanding, right thought, right speech, right action, right
  livelihood, right effort, right mindfulness and right concentration.


From this, it is widely assumed that to end suffering, we must end craving and that's it.

However, according to SN45.179 and SN45.180, it is not just craving that must be ended, but also the ten fetters, through the Noble Eightfold Path.


  “Bhikkhus, there are these five lower fetters. What five? Identity
  view, doubt, the distorted grasp of rules and vows, sensual desire,
  ill will. These are the five lower fetters. This Noble Eightfold Path
  is to be developed for direct knowledge of these five lower fetters,
  for the full understanding of them, for their utter destruction, for
  their abandoning.”
  
  “Bhikkhus, there are these five higher fetters. What five? Lust for
  form, lust for the formless, conceit, restlessness, ignorance. These
  are the five higher fetters. The Noble Eightfold Path is to be
  developed for direct knowledge of these five higher fetters, for the
  full understanding of them, for their utter destruction, for their
  abandoning.


So, why is craving singled out in the third noble truth, rather than including all of the ten fetters?
Craving cannot be eliminated at will. You need to do something to eliminate it. That is what the fourth noble truth is about. In other words, one needs to cultivate wisdom to eliminate craving. Elimination/weakening of fetters are the mileposts of developing wisdom.