to pick-up the centralized server/client problems from the last post again (seen in  for instance). i have found a very convincing example where this p2p usage would make much sense. the wikipedia project has lots of costs related to bandwidth usage and server load. in a p2p like webservice this load -> therefore cost, would be distributed to the clients.
this technology as in  is very young and we have to alter the way we use technology today in a very invasive way but it can be done. look at what google does with ‘gears’ for instance (altough this is not p2p related) it is a very different concept compared to already existing use cases. the same goes for web 2.0 ajax technology which is now widely deployed.