Before Shakespeare, Chaucer. I have only read him in translation, but I put him somewhere doing the unimaginable. First, that poetry will always be with us. The aim of the lyric poem is to show what is going on in the theater of the private mind when you are alone in your room. I think people will always want to explain to themselves what is going on in their own heads and then to put it into language, whether prose or poetry.
Poetry offers a more concise form of that inner drama than prose.
Poetry is casting reality into a symbolic form. You can't just write life down. I think that's a human activity that will always continue. The muse lights in different countries at different times so it's impossible to say where she will light next. The next great world poet may be an Indonesian.