Curtain walls have certain advantages. The main one is appearance, followed closely by maximized glass for daylighting. Another advantage is that erection can be done as fast as any other system.
In my experience stages fall into two broad categories. Traditional Theater Stage (proscenium, arena, thrust) includes stages that are used for plays, musicals, and dance; and Platforms include stages that are devoted to only speaking, town meetings, video and presenting.
Stages can be designed for a specific purpose, e.g. drama, musical theater, dance, or musical performance; or they can be multi-purpose. Once you pass the limits in the building code for a Platform, there are several 'triggers' for specific requirements. Take a look at Chapter 410 of the International Building Code.
The type, size, flexibility and sophistication of the venue (whether Stage or Platform) is dependent on the function and end user: Amateur/Professional, Primary/Secondary School, University/Professional Theater, Broadway Touring House or Regional Theater. All of these considerations will affect the design criteria much more.