I've been reading Dionysus Writes: The Invention of Theatre in Ancient Greece, by Jennifer Wise. Its standout thesis is that there's a reason why the Greeks didn't have theater until they had a working alphabet - namely, that you need popular literacy for the practice of theater to blossom.
The older Greek poetry was from a more purely oral tradition - the epics and the lyrics, Homer & Sappho & company. You just needed one performer for these things - one specialized virtuoso of memory. Storytelling is an art as old as humanity, and it includes some acting, but it doesn't involve actors exactly.
In theory you can imagine Prometheus Unbound being composed orally, and taught orally to actors. In theory. But the technology of an easily teachable alphabet made it much more feasible.
To get theater right
In practice you need
Playwrights who write
And actors who read.