Of course you can (ab)use a lot of protocols in various ways, however, XMPP was designed with this extensibility in mind and that's exactly why its basic RFC is so minimal. Heck, even basic instant messaging over XMPP is defined in a separate RFC (RFC 6120 for Core and RFC 6121 for XMPP-IM).

GP already stressed it out:

> Matrix's main data primitive is synchronising conversation history within a room - not message passing.

So Matrix might be well suited for things like blogs, but XMPP will be certainly better for push notifications, for instance. However, you can easily build Matrix-like primitives on top of XMPP, while the other way around will be less flexible.