It is not possible for users to access the filesystem on the iPad since this access is not permitted on devices running iOS.
- How is the function of the iPad improved by preventing users from accessing the filesystem?
First, I think it's about how people think about their workflow. It's an emphasis on "how" instead of "where": http://www.malcolmgroves.com/blog/?p=633
Windows has been promoting the doc-centric view of the world for a long time. I remember that being one of the supposed big advantages of Windows 95, the ability to focus on your documents and not the apps that create them. File associations, OLE embedding, etc all attempted to push people this way. Yet my experience suggests most users resisted it, or missed it altogether. For example, I still much more frequently see people start Excel and create a new spreadsheet, rather than use the Start Menu option (or right-click option in Explorer) to create a new document. Most users still seem to think in terms of applications, not documents.
If you are primarily interested in creating a spreadsheet, you create the spreadsheet first. What you call it and where you put it come later, or in the case of iOS that step is removed entirely, you just don't have to think about it at all. On the other hand, I see people editing particular files on their desktop all the time--it's no longer I want to create a spreadsheet anymore, it's I want to edit this spreadsheet.
Second, I think it's also a matter of simplification. I have a lot more files on my computer than I do applications, and I don't necessarily want to sort and organize them so I can find a particular spreadsheet that I'm interested in. Taking away the documents and just focusing entirely on applications, which filter you down to the documents they know about, simplifies things.
Third, if your focus is consumption, does it matter as much to you where your files are? I think maybe not, and the iPad and the iPhone feel like consumption devices to me. If something doesn't matter to the target audience and it's just adding unecessary complications, maybe it should be taken out.
From the comment "this is a philosophical question that doesn't have an answer" - Yes, it indeed is. The philosophy behind this is Steve Job's obsession to be in complete control over the user experience of the device. By allowing access to the file system, Apple is relinquishing control to the user, who may be a bit naive and do stuff Apple may not want to encourage (for example - install "unapproved" apps, hack the OS and experience crashes, viruses etc.).
The whole idea is that Apple believes it knows what the user wants, better than the user himself.