Roman Jakobson wrote eloquently about the insights which linguistic analysis could bring to our understanding of poetry and of the importance of poetry to a full understanding of language (Jakobson 1960, apparently his most cited article ever).
These days many working linguists stick to analyzing more prosaic utterances, but a few still keep their hand in the game.
There was a recent kerfuffle at the American progressive political periodical The Nation when they published a short poem by a poet named Anders Carlson-Wee which imagines a homeless person in the first person, and uses turns of vernacular closely associated with African Americans (such as copula drop—as in, “if you a girl” for ‘if you are a girl’). Pockets of the internet erupted in indignation that a white poet was appropriating a black voice and the The Nation’s poetry editors prostrated themselves before the mob, disavowing the poem and appending a “trigger warning” to it for “giv[ing] offense and caus[ing] harm to members of several communities.” The poet apologized for the offense and harm caused.
John McWhorter, professor of linguistics at Columbia University, has published a thoughtful defense of the writer’s use of language in the poem in the periodical The Atlantic which seems to me to be very much in the spirit of Jakobson 1960. McWhorter trains a linguist’s eye on the poet’s use of African American Vernacular English or Black English, and comments on it in the broader social context. I think it’s a nice example of how linguistics can provide an informed perspective on matters of current public interest.