Actually, it's not just iTunes that suffers from an iPod/iPhone legacy but iOS itself. I think that iOS inflicts lots of limitations on the iPad that originate from its smaller cousins.
The iPod gave us iTunes and unidentifiable files names (in the name of DRM?). Other "MP3" players just use a standard file system with songs organised into folders, much simpler.
The iPod Touch and iPhone gave us chunky icons. a simple (simplistic?) "desktop" and apps designed for a smaller screen.
I am not sure that any of these compromises are appropriate for a tablet. As someone said, the most obvious manifestation of this are the "HD" versions of iPhone apps for the iPad. They often do little to make serious use of the larger screen size, they just fill it up.
Forget "it's not supposed to be a computer, I think that this is the real reason for some of the iPad's limitations.