Nonsense like this comes up every so often and it's always based on a myopic and naive view of computing, and of the general public's use of computers.
File systems are necessary because files need to move between applications and devices. File systems are already an abstraction, and they will continue to be useful until someone comes up with a better one. Which, at this point, seems unlikely.
Yes, your exposure to the file system on an iPad is much lower than on a MacBook Air. But it's still present. Try saving an image from the web, an email attachment, or using the Drop Box App. You may not be at a command prompt but you're dealing with the file system.
The more complicated things you want to do with a tablet, the more you're going to have to interact with the file system. A better abstraction does not yet exist, so the file system persists.
Declaring its death prior to the appearance of a better abstraction is silly.