first off and most importantly, flash cameras are dangerous to the cast. They need to be able to see where they are going and if they are blinded by an unexpected flash going off in their face then they could become disoriented and injure themselves.
Another reason is that the flash ruins the theatrical experience for the rest of the audience. Not only is it distracting but it also ruins the lighting effects on stage
and the last reason is a legal one... it has to do with unauthorized use of images. It's all very legal and I won't go into it here. Equity I believe specifies in their contracts that unauthorized photography and recording (both audio and video) are prohibited.
So if you want photographic images, you'll have to settle for purchasing the souvenier program
Ignorance killed the cat....curiosity was framed