No, it isn't impossible at all. However, it would be very subjective- like that Freenet overlay software that eliminates SPAM and child pornography with ease, such a system would be more based on subjective webs of trust and optional lists people could subscribe to, used to determine what you see.
The sender anonymity part could just be having every node act as part of a mixnet- wait until you receive X messages and/or Y time has elapsed, shuffle messages, send them out to randomly chosen nodes, repeat this for 3 hops and then your message is propagated.
I've wanted to make something like this for ages since 4chan has gone so downhill. Perhaps it should happen then. It would probably be easier to adopt than something as complex as Freenet FMS for sure.
I would most of all hope it would solve the problem of people asking such questions, by making them perfectly moot. Folks would be forced to settle for wistful speculation about what the world might have been had the thing not been created.
Trolls would need to avoid being too overtly inflammatory, lest they get blocked by kneejerk reaction.
> What problem would it solve
Well, we could have a bunch of discussion boards again, ones that aren't at the permanent whims of profiteers or atrocious moderation. And strong anonymity even against global passive adversaries. Clearly there is a case for it, I know a lot of people who would find lots of joy in such a thing!
The sender anonymity part could just be having every node act as part of a mixnet- wait until you receive X messages and/or Y time has elapsed, shuffle messages, send them out to randomly chosen nodes, repeat this for 3 hops and then your message is propagated.
I've wanted to make something like this for ages since 4chan has gone so downhill. Perhaps it should happen then. It would probably be easier to adopt than something as complex as Freenet FMS for sure.