That is exactly the point why Matrix is great for organizations. You can run your own Server and your members can communicate internally and with members from other organizations that run their own server too.
In practice telephone and email (and web portals) are still the way to go for external communication and Matrix only shines for internal communication at the moment.
The public services are nice for individuals, but I don’t see a real benefit in Matrix if you are using those, because there are other public communication networks for individuals, that are just more accessible and more wide spread.