The albatross in the poem is described as a bird of good omen. There is, therefore, no need for the mariner to kill it. Given the religious symbolism of the poem, and Coleridge`s own understanding of Christianity as immanent in nature, one can even think of the albatross as a sort of type (in the sense of typological interpretation) of Christ, an innocent and unstained being that acts as a scapegoat for fallen humans.
The penance assigned to the mariner, which involves spreading his tale and a message of universal love, is like the task assigned to Christ`s apostles in the Great Commission. The mariner, despite being a fallen human (like doubting Peter) eventually becomes a messenger and an instrument of others people`s redemption. Thus punishment in the poem is not seen as simply a sort of eye-for-an-eye exchange but rather as an opportunity for redemption through suffering.