I suspect the "exoskeleton" or "persona" or whatever you want to call it works pretty much the same way for things like readings, presentations, plays, etc.

I sing in front of people for a living, so my anxiety over that is typically very low. It's the same for reading. In both cases, I have text or music in front of me that I have written, practiced, or memorized. If I follow the "script," there is a limit to how big a fool I can make out of myself. I don't really mind giving presentations either, but I really like having things written out in detail as much as possible. If not, I tend to babble.

Giving a talk, reading, or performing where I know what I am going to say or sing is a completely different thing from having to walk into a room of strangers and improvise what I'm going to say or do.