I suspect that music like an orchestra requires vastly greater precision than is required from plays. For example, if the orchestra is going to become rapidly

I suspect that music like an orchestra requires vastly greater precision than is required from plays. For example, if the orchestra is going to become rapidly silent, or loud, in a dramatic way, then it's important that all of the instruments do this on the same timing. You can't have an instrument that "false starts", or it will sound obviously out of place. By comparison, in a play there's a lot more leniency and flexibility. Typically only one person is speaking at a time. If one person pauses for a few moments between lines, or enters/exits stage more slowly than normal, that won't disrupt the rest of the play -- whereas if any musical instrument hits at the wrong time, it will.