The tricky part with that system would be that you'd also need some new mechanism to retrieve the files. Instead of the regular WWW stack, you'd need something like a massive distributed hash table that could handle massive distributed querying and transferring the hashed files. Many P2P file sharing systems are already doing this, but a sparse collection of end-user machines containing a few hashed files each isn't a very efficient service cloud. If every ISP had this sort of thing in their service stack or if Amazon and Google decided to run the service, all of them dynamically caching documents in greater demand in more nodes, things might look very different.
This would mean that very old hypertext documents would still be trivially readable with working links, as long as a few copies of the page documents were still hashed somewhere, even if the original hosting servers were long gone. It would also make it easy to do distributed page caching, so that pages that get a sudden large influx of traffic wouldn't create massive load on a single server.
On the other hand, any sort of news sites where the contents of the URL are expected to change wouldn't work, nor would URLs expected to point to a latest version of a document instead of the one at the time of linking. Once the hash URL was out, no revision to the hashed document visible from following the URL would be possible without some additional protocol layer. The URL strings would also be opaque to humans and too long and random to be committed to memory or typed by hand. The web would probably need to be somehow split into human-readable URLs for dynamic pages and hash URLs for the static pieces of content served by those pages.
I'm probably reinventing the wheel here, and someone's already worked out a more thought out version of this idea.