It says "screenshots of themselves". The application is responsible for rendering the screen in the first place so it fundamentally doesn't need a permission.

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)

Doesnt android already have a "network" permission? On some roms you can enable it/disable it on install of the app even

No, it has a "full network" permission. It's not at all difficult to bypass it if you control both ends.

GrapehenOS has that. It asks every time you install an app if it should have network permissions.

I mean yeah technically the website can’t screenshot, but it can do many functionally equivalent things.

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?

Well, blocking javascript would stop that. Noscript is a thing that some people use.

For an increasing plurality (possibly even majority at this point) of sites where the purpose is not purely to read text, this is effectively equivalent to saying "you can just not use the site."

Ublock origin also has that ability

All I/O (including timing, date/time, internet, and everything else) should be behind permissions (although some may be permitted by default, they should still be overridable). Furthermore, all I/O should allow the user to program proxy capabilities (which can be used for testing error conditions, as well as for privacy and security, and for finer permissions, and logging, and other stuff).

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.