This could be an alternative to some of the instant messaging systems that provide privacy but not anonymity.
I know that some chat messaging systems can use Tor as the transport, but they have problems of their own.
What I'm thinking about is something along the lines that each user app hosts a hidden service that receives messages through a standard HTTP API. Users need to hand their hidden service address to friends. The protocol itself already handles payload encryption and routing but messages could be further encrypted at the app level before being sent (using the other user's public key once an initial exchange has been done).
Granted, sending a message would require all parties to be online at the same time, but there could be a set of relay servers to hold messages until they get fetched.
I'm sure there are lots of hairy issues to take into account, but I would expect the existing protocol to mitigate some of these compared to a ground-up approach (like Session is doing). Tor is fairly mature and, despite all attacks on its infrastructure and protocol, it is still standing.
I'm also wondering if such a messaging system couldn't be useful for some IoT types of scenarios, as it would protect the location and communication of the source of the data, so the devices could not be easily physically found and hacked.
None of this would be useful for high-bandwidth real-time data, but you can get reasonable latencies and traffic sent this way.
Maybe it's all just a dumb idea...