Although this is an interesting, novel method, there are so many fingerprinting capable APIs in native code that I don't think this matters much. Many apps I use daily require internal storage permissions and a bunch of them drop random dotfiles with magical IDs in there. Xiaomi even dumps a world readable unique device ID on the emulated SD card. Not all apps require external storage permissions, but even then there…
Why can't these apps be restricted to certain folders you need them to access?
I also feel like apps which abuse file system permissions to modify the user file system (e.g. create files useless to the user), let alone the system file system should be reported and banned.
Any app should have full rights to write anything to a special directory dedicated for it however. But you can set up a script to purge it or delete specific files from it on a schedule.