For two messengers operating on two different encryption protocols the only way to talk to each other is to introduce an intermediary, which will decrypt and then re-encrypt messages, thus throwing p2p model out of the window.

Some optimists here telling that all messenger might follow a certain "standard" for transmitting encrypted messages. And in fact some messengers might, but this standard will be the lowest common denominator, i.e. the weakest security protocol all know.

For p2p model generating secure private key is paramount. Can this be guaranteed by every peer operating in a chat? Not unless they all made by the same team with high security standard.