"Trivial file conversion" tool can be implemented the same. The app tells the OS "hey, I want some files to convert" and the OS either grants access to a set of files/folders, or queries the user which file(s) (s)he wants to provide. IE the "open file" modal is the only window to accessing files. You can think of it like the HTML5 File upload & Drag/drop APIs, but a bit extended & more user-friendly.
Obviously smart engineers can think this through for longer than 3 minutes like I just did, and come up with better/user friendlier/safer solutions. But it breaks all backwards compatibility in almost any desktop OS
Only my backup tool gets root and can access other application's data - random trash games I download or even if I were to install them from pirated sources are unable to do that.
It's a vast improvement at the very least, even if not a perfect one.