I don't think anyone today could recite Beowulf from heart. But 1500 years ago that's exactly how it was enjoyed.
Look at these people that will declaim Pi digits, just because.
Also there are difference in education over different cultural era, not only through time but also space. I heard that India for example value more repetition, where western culture is more in love with innovation. These are of course nothing like exclusive tendencies.
Now if you look at antic Greece, it's certainly not like everyone would be able to restitute Homer word for word. Actually it's easy to forget how divided in term of linguistic and social classes this societies where, and focus solely on the most renowned figures as if they where all part of a tight social group full of solidarity and genius. Actually even a guy like Hippias of Elis can be both depicted by plato as exhibiting all the tremendous admirable feats of the time, including mastering the art of mnemonics, and yet turned into a clueless bragger that isn't even able to recognize that he just doesn't know how to define beauty.
Is this the case? I was under the impression they memorized the plot beats and filled in details on the fly. Also using set phrases or epithets like "Gray-eyed Athena" to slow down the narration and let them plan further.