Why? E-Mail and Jabber work the same way. Everyone can run their own server, and many do, but most users prefer to use someone else's server(s).
Sure it can work that way but is that the ideal? Doesn't that make the network less robust and more vulnerable to attacks and manipulation? What happens if some attackers start running a cluster of supernodes? The main point is why rely on this more vulnerable architecture when you don't have to? It isn't easier to implement.
Edit: Even more closely related: Kazaa and Gnutella work the same way, too. You connect to a supernode that then searches for files on your behalf.
Yeah and I would argue neither of those systems are very well designed. Limewire replaced the gnutella routing with Kademlia actually.
spaceshaker: yes I agree there will have to be nodes that act as proxies for mobile devices.