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.
“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?