> There is no easy way to close this privacy opening
Sure there is.
Hide screenshot taking behind permission and slap down hard apps that refuse to operate without them.
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Now, what could reasonably be a permission is "access the internet", but our overlords don't approve of that thought.
(Contrast this to web pages, which do not render themselves and thus can sensibly be blocked from screenshotting)
For example, it can capture the entire DOM and send it off, including the contents of input fields that have not been submitted.
That DOM capture can be replayed on a browser to show what the user sees. So what’s the difference?
However, if an app wants to make a screenshot of itself, then it could do so by emulation of itself (so no permission is needed), as long as everything it displays is rendered by its own code rather than calling other functions in the system to do so.