Why would a director consider an amphitheatre?
This is a good question. There are number of reasons why a director might choose an amphitheater. Let me name a few of them.
First, as the person above stated, amphitheaters have good acoustics. Keep in mind that this was the theater of choice for thousands of years for the Greeks and Romans. They learned a thing or two about plays and performances.
Second, an amphitheater has a certain ambiance. For example, if a director wanted an outside venue in the night under the moon, then he or she could do no better than an amphitheater. There might be other artistic reason for this as well.
Third, from a more practical point of view, costs might be an issue. It would be cheaper in some ways to have a performance at an amphitheater than a concert hall.