We've had this since 1988. Its name is IRC. Anyone could communicate on a protocol shared by any kind of app you wanted (not that I'm arguing that IRC is the gold standard of chat protocols necessarily - Matrix seems an improvement to me - but it was an open chat protocol before most of what we now think of as the internet existed). The fact commercial chat apps aren't interoperable is a decision they made to screw the user for corporate interests (i.e. force everyone who wants in on the network onto their app that they can track and advertise on), not because cross-app communication is a new or novel concept.
But yes, I believe this is the way to go. Unfortunately it will never be the way the mainstream goes because the ad money from the walled-garden apps funds their own marketing campaign to keep them in the forefront of users' minds, but both ecosystems will probably exist side by side in perpetuity (at least until the walled-garden lobbyists convince the government that open apps have to be outlawed because of children or terrorism or something).