>I’m presenting from a presentation, I want to switch to a live demo environment, and to do so I need to turn off the presentation entirely?

Ideally, a well-designed live demo app would also support presentation mode. Switching to it (e.g., via Alt-Tab or swiping) would automatically update the external display.

The external screen would act like a dedicated full-screen view for any app in presentation mode. If no app is in that mode, it would stay blank (not show the home screen) - unless the home screen itself has presentation mode enabled.

Anyone preparing a presentation should and do tend to set everything up and test it in advance. Apps that support presentation mode can keep control of the external display and let you switch between them smoothly, so all that preparation pays off.

Not a live demo app, a live demo environment for an app. Your suggestion would mean every app would use presentation mode, which makes the concept worthless.