There are still people who try. There are videos online of people who have memorised the ancient Greek (with modern accents, of course), like https://youtu.be/Zzal-36eIoY. I think at some point Boris Johnson of all people started reciting a bit of the Iliad during an interview at some point.

Don't expect the full version on Youtube, though; the 24 books seem to all take an hour of each, and I don't think anyone has cared to spend a full day reading ancient Greek into a microphone yet, let alone recite it for an audience.

Unfortunately, I can't really find an audiobook version of the English translation of the Iliad. Perhaps AI can be used for chores like this, as human speakers would probably lose the rhythm often, which I imagine must make accurate audiobook recordings in this style quite difficult.