Why might a poet referance an ancient myth in her poem?

I've never seen that, a poem would should allude to something without any referencing. Poems are supposed to be about emotion and not bothering whether someone gets it or not. Allusions usually aim at the literary elites, who would only know the allusion, in order to elevate the poem to an elitist status and making it more valuable.

Mythology contains universal human truths expressed in symbolic form. For example, Sisyphus condemned to forever roll the great stone up the hill only to see it roll back to ground level over and over again may be seen as an allegory of human endeavour.

A allusion (reference to a famous or well known event) is common in poetry.
It helps give the reader a better understanding of a feeling, event, or just any subject in context by comparing it to a already well known event or story.