Yes. And an app could render the same thing on your screen via the same tech currently used to robustly watermark generative AI image output, and now not only you won't be able to screenshot the app, you also won't be able to take a photo of it with another device, and on the off chance you found some pre-202X camera that still could, no other computer would display the resulting photo either.

Yes, let's keep coming with more of these great ideas.

To cut this short: the whole overall idea is just universal DRM writ large. A big, principled no fucking way, ever from me.

But what about the personal privacy / venue rights ...

That's a social problem, it should not be used as excuse to give unilateral control over other people's technology to groups or individuals with special interests.