Are there any ancient historians/writers that discuss Greek Drama?
Your best source for information on ancient Greek Drama is Aristotle's "Poetics". He was what we would call a descriptive critic, which means he described the theatre that he observed. He gives excellent descriptions of the elements of theatre, the structure of the plays, and important concepts like catharsis.
Aristotle didn't write a great deal about the actual production of the plays, however. For that, you might find a copy of one of my favorite books - "A Source Book in Theatrical History" (edited by A.M. Nagler). This book is a collection of primary sources on theatre throughout the ages, but the opening chapters are about Greek Theatre. They provide excellent detail about the production of the plays and the production values used. This book should be in most libraries, I expect.
You should also read Plato's Republic. In books 2, 3, 10, Plato offers his rationale of why there should be no poetry in his ideal republic. A basic summary is as follows:
1. Poets write under inspiration, and not by using reason. This is important, because what Plato aims for is reason.
2. Closely allied to point one is the idea that poet is often ignorant about what it teaches, and so teaches incorrect things. This can possibly lead to corrupt people.
3. Perhaps, one of the most famous reasons: Poetry is a mimesis, that is, imitation. This makes it inferior not only to reality, but more importantly to the forms, something that Plato has much to speak about.
4. Finally, poetry encourages the wrong emotions in people.