I'm amazed when people talk about limitations of an iOS device. There is nothing that an iPad Air can't do that a medium laptop can. It all depends on the application. There are several very complex apps on the App Store that do amazing things. I hear a lot od people complaining they can't access iOS file system. The thing is: you don't need that! Simple apps will not expose it. Complex apps can expose it by either working with local folders or cloud folders. There are plenty of apps that already do that. Apps like GoodPlayer, for instance, allows you to save videos locally or remotely and you can structure it in foldes. There are several methods of retrieving and and saving files. If an app doesn't allow something, it's not a limitation of the OS, it's the applications itself. iOS has several ways to share and transfer files between applications. The developers of the applications need to know how to do it. The most updated form of sharing files is through the cloud. Mobile devices can do that very well using services like Dropbox, iCloud, Google Drive for simple applications or Amazon storage, etc. for business. I sincerely can't see any business application or process that can't be implemented in an iOS device.
You provided an excellent explanation of what is wrong with iOS and/or the iOS ecosystem. Just look at how many layers of complexity your explanation of why it isn't possible and what potential solutions could be.
Here is the solution on Android:
1. Install Dropbox or Google Drive. (I like Dropbox because I dislike Google)
2. Hit reply on an e-mail.
3. Click paperclip. Select dropbox. Select file(s).
4. Send mail.
It isn't that this task is too complex for a device. Competing devices/operating systems build this into their basic applications. Only Apple sends you on a goose chase to find a half baked third party solution to something as simple as attaching a file.
Perhaps this isn't an operating system problem as you said. This is an app problem, given Apple's "sandboxed" architecture where the app controls the files. But it is still an Apple problem because their mail client doesn't provide for this basic feature AND their method of sandboxing of apps makes it hard for third party developers to support this feature.
As a note, I do own GoodReader and Quick Office so I can "see files" on my iPad. These are considered the best apps out there for productivity and file management. In both apps I still can only send one file to the mail program, which opens a brand new mail with that one file. I then have no way of easily adding additional attachments. Further, I am not looking to send a new mail - I am looking for the simple function of "reply all and attach".
I realize I am harping on this one mail issue. There are others. When you step outside of the iOS ecosystem for just a few days you realize how all of these little quirks that we come to believe as "not meant for a tablet" actually are super convenient (and totally possible) to get as a feature elsewhere.
I'm not a Google or Android fan as I stated. But Apple can't have their head in the sand about what their competitors enable users to do (even inside core apps like Mail). They are risking potentially going down the path of the Apple of the early 90's.