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There is a simple solution to this. I'm a software engineer/designer by trade, so here's how I'd solve it without getting in the way of the elegance and simplicity of iOS.

Add one single feature available to any application:

"Share with other apps"

When you do that, a link to that data is made in your "Files" browser (which is available to apps that support it). Any app that is able to read that type of file, will then be able to see it when you access the "Files" section.

Problem solved. Steve, pay me.

Doesn't the iPad/iPhone already have this option? It's called "Open in..." and your apps can share these files with each other.
 
Doesn't the iPad/iPhone already have this option? It's called "Open in..." and your apps can share these files with each other.

Yep, but the way I understand it, open in creates a copy of the file. So if I had a 500mb video file and I opened it in anoter app, I'd have just doubled the amount of space taken up.

The other posters idea is to create shortcuts, so the amount of storage space is not changed...well okay maybe by a kb or so, but you know what I mean.
 
Apple will probably resist providing real file system to users as long as they can because doing so will cause MacBook cannibalization. On the other hand, since competing solutions (Android, Windows etc.) do offer this feature rendering iPad an inferior product, Apple will not be able to sabotage this for too long.
 
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