You get to know a poem so much better when you memorize it. You need to think about each word. Sometimes your brain wants to substitute another word and you have to think about why the poet chose the one they did instead of the one that might feel natural.
It feels like engaging in a great conversation. These poets all read each other's work, going back in this timeless chain into the distant past. And you can tell when one is responding to the words of another, who they know can never answer back, but there's a connection all the same.
Recognizing Ozymandias being recited in a Ballad of Buster Scruggs short felt like seeing a dear friend make a surprise cameo in a movie.
Plus, if you've got a flair for the dramatic, it's a neat party trick.