A copy, not THE copy, of a file. Of course, then you get into locking and updating issues. I'll be surprised if there isn't a CVS pserver or similar lurking under the covers of the first P2P app to make it big in business. Then the P2Pness would make a data finding mesh which pointed to a much smaller mesh of places to actually get the data. A compromise from both perspectives, but one which is much more maintainable in the long run.
Servers are servers for a reason.
If you care about always getting to your data, you have to do certain things, and those things are not desktop kinds of things.