> When it asks me to open a file, or a directory, it should invoke a system dialog that cannot be faked, and when I pick a file/directory for it, that directory or file should be bind-mounted into its mount namespace without giving it extra information about other files beside it, or indeed what's the full path of the file. When recording a screen, I should be able to pick which regions and which applications it should be able to see, and the system should make it think it's all there is.

You've described exactly what flatpak is doing? I'm curious what gaps you see with its approach in particular.