Poetry has been labeled a dying art for almost as long as it has existed: It’s not what it used to be, and nobody reads it. Shakespeare’s contemporaries wondered if English could ever equal Latin. American poets of the 19th century wondered if they had been superseded by prose. Each time, the doomsayers were at least partly wrong: Shakespeare’s era had Shakespeare; after the death of Longfellow came Marianne Moore, T.S. Eliot and Langston Hughes.

Today the complaints come online. “Insta-poets” like Rupi Kaur, whose legions...