You couldn't be more wrong. They do not use the legacy file system as you know it. They use a task specific file system. It's evident in every aspect of iCloud, and iTunes.
You're bewildered. The device uses a filesystem just as we know it. The user doesn't get to see it, but it is there. Additionally, there's a filesystem exposed to the user that consists of app-on-desk and/or-app-in-folder; this is horribly broken, but nonetheless allows the user to organize apps in the way that the computing community has long determined to be desirable.
You should ask yourself this: Why are there named user folders in iOS in the first place? There are two obvious reasons: to reduce clutter, and so you can *organize* your apps: games, photography, etc. To argue that organization at the user defined level isn't Apple's goal is ridiculous, that's exactly what the folders have done all along. They just have not done it well. Now that the count limits have been sundered, they'll be better; but you mark my words, these other limits are also impacting the device's ability to do work, and creating one-app-only zones where anything that can be done to a file must be in the one app that owns it, with the notable exception of the photos, where Apple has made the mistake of again creating a unique filesystem for them that doesn't benefit anything else. It is form over function, and it's well known to be the wrong path. Why did it work with iOS at all? Because these devices started out as non-general-purpose computing platforms. But now they're much more powerful, and so they're going to have to come with a general purpose filesystem to complement them. There are several ways to do that, but the current implementation is only a partial image of one of them, and amusingly in the case of your arguing position, it's a limited version of the bog-standard computer filesystem we're all familiar with.
You see the files specific to the task you are working on.
No. You don't. That's part of the problem. If I have a text file, there should be all manner of apps that might have business with that file. Text editors. Log viewers. Spellcheckers. Many more. But because the paradigm is primarily app-owns-file, this sharing is crippled. You can't use the synergy of multiple apps to work on files, and that shoots the device, and the user, right in the foot. If, on the other hand, one could organize one's data and access it via that organization, without relying on a broken idea of app-owns-document, then that synergy would be brought up to the level of a modern computer system. It's a failed, crippled vision and Apple has already begun to revise it with iOS 7. Further, not only should apps be able to see whatever files you want them to, you should be able to put one swatch of (for instance) text files in one folder, related to one task, and another swatch for another task in another folder. This prevents you from having to wade through every file for every task that you ever did.
I'm not looking at it from the perspective of a "geek", as you wrongly assume, or the least bit concerned about multiple shells, etc.; I'm looking at it from the perspective of a business owner for whom the functionality of iOS falls far short of what I need just with conventional file management for mundane, non-geeky files. Would geeks benefit from such changes? Sure. Would the left side of the Gaussian be bewildered and lost? Unlikely. The existence of the ability to create subfolders does not have to be used. The search facility is still there, much like Spotlight exists on OSX. You *can* use such a system like a drooling idiot; but it makes no sense whatsoever to limit everyone to that status.
Imagine the iOS device after years of use. Full of files, many perhaps of the same name. You search for "mom" but there are 40 instances. Which one is the one you want? Without folder organization, how can you tell? This is just one of the obvious pitfalls. We need date; we need organizational context; we need sharing among apps for all files; we need limits lifted and tree structured folders implemented. And it's going to happen or Apple will be left behind. Mark my words, I've been watching computers since the 70's and there's just no way going back that far is the way to go.