There is nothing preventing my shiny new iOS app from sharing files with other applications. Apple is just preventing those files from being stored on the device. Instead, if an app developer wants interoperability, they can have the app save a file to Drop Box, or my Google Drive. Any other application can access that same cloud storage and access the file.
The beauty is we've moved beyond sharing between applications on a single device. Now EVERY application I run on EVERY device I have has the potential to share the same data seamlessly.
This is why iOS doesn't open its file system. It wants the app developers to use something a little more flexible and reliable.