All the apps require all the rights. If I do not give them the permissions they won't run. So I have no choice, I have no security then and I cannot store any valuable data on the phone.
Why the apps are lying they need global files access to only store their own data? I have found in some Android SDK doc they can store their own data even without global files access.
Other apps could provide functionality without that specific feature but they refuse to run at all unless they get all the permissions they ask for.
Even opening local files could be done safely by an Android-provided dialog box, without giving uncontrolled permissions to the whole disk.