Reliability could be improved if all required functionality is P2P, as the program would not need to rely on a third party server. Of course, this assumes that the party/parties on the other end of the P2P connection are online, which is the downside of all P2P services.
Another underrated benefit of P2P (if implemented in good faith) is that the users will have peace of mind with regards to the ownership of their data.
> if implemented in good faith ... users will have peace of mind with regards to the ownership of their data
Famous last words! Not sure how users will establish the trustworthiness of P2P protocols (and there will be many competing versions), when now they cannot determine the trustworthiness of one service.
Messaging, chat, video calls, and gaming without the need for a centralized service. All you need is a directory so you can find the other party. Like Skype before Microsoft.