I agree with you for the most part. The problem that currently arises is that you have to open up an app to get at a file, but that app can't see anything but its native file type. If there was a catch all file system "app" you could go there to open files, and the appropriate app would open it automatically with one tap. Tap and hold would bring up the option to "open with/open in" some other app than its native one.
Basically I think the way dropbox works with iOS is excellent. That's all that's needed, really. iCloud already works the same way but it is either on or off, so you either save everything locally or nothing, and you can't keep different file types that are related to each other (such as projects, like "Corporate Budget 2014" with Numbers, Keynote, PDF, notes, etc) in the same place, meaning you have to duplicate iCloud folders and other file system resources like dropbox, because saving things in iBook is a nightmare.
One way of looking at it is that is is an app based storage system as opposed to a file based storage system. Its just that it doesn't seem this is the most efficient way of organising things for productivity, though for consumption it makes a lot of sense, as movies, magazines, books, comics, songs, etc. feel natural that way because you almost have been storing them that way already.
This is just my humble opinion of course, but I feel that Apple has been a bit too short-sighted here, as the implementation of the file system seems more consumption centric than creation centric, and even though I can literally do every single thing I need to do both personally and professionally on an iPad, it is a much more cumbersome workflow and not nearly as efficient as doing the same stuff on my MBA.
The way to streamline this is to actually give proper desktop implementation of multi-tasking (iDevices are powerful enough for this nowadays) as well as inter-app communication, and a better implementation of how they envision the file system working in a productivity centric environment.
