Sometimes it never happens.
Sometimes poets take on personas - like computer avatars. And assume that personality for individual poems (Browning springs to mind with My last duchess et al.) or a series of poems or some poets even return to that character again and again like Yeat's Crazy Jane.
Usually a poet's voice is a character too. How they come across in poetry is not how they are in real life - thank goodness. However later when the poet is dead, the two can conflate. Now some think of Sylvia Plath for example as neurotic or even mad thanks to her later poems and the Bell Jar; when she most often appeared as driven and organised to her peers.
If you are struggling to find your voice, assuming an avatar can help - just as it frees one up in gameplay. The avatar or characters you assume will probably be the building blocks of your ultimate voice.
So it is worth exploring. And you may find that you encounter these characters again and again just like WBY.
btw avatar as a word has a lovely origin in Hindu religion where it means a deliberate descent of a deity to earth, more literally translated as incarnation or appearance.