There's no centralized server. There's a server with the majority of users for now (in matrix.org), but the network is decentralized, with many servers. The server implementation run by the majority is called Synapse, but there are others (Dentrite, Conduit, Construct..).
I'm puzzled by this comment. Can you elaborate on what you mean by phoning home?
Are you talking about https://element.io, which points to matrix.org homeserver and signing server, etc?
In that case, well, just use a different server and your own client. Or self-host, and select one of many clients: https://matrix.org/clients/. That's the whole point of federation.
You can even deploy your own web client pointing to whichever server default you want, many people do. E.g: element.debian.social, chat.mozilla.org, etc.