In Plato's allegory of the cave, why can't the prisoners move their necks or legs?

Within the Allegory of the Cave itself, Plato holds that the people in the cave are bounded in place "with their necks and legs fettered, able to see only in front of them." Within the allegory itself, they're physically restrained, unable to move.
As far as the deeper questions of why a society would choose to have people restrained in such a manner, I'd suggest that such questions are actually irrelevant to Plato's allegory. Ultimately, this allegory exists to illustrate Plato's ideas concerning the soul, the material world, and the philosopher's journey towards knowledge. The prisoners in the cave serve as a representation of the human condition. Just as the prisoners remain trapped and fettered, unable to interact with anything more than shadows, ignorant of the truth of their condition and of the reality surrounding them, Plato holds that the same applies to all human beings, trapped as they are in a material existence.