XMPP is focused on real-time, synchronous communication. It does provision for async communication with server storage of offline messages, and even originally

XMPP is focused on real-time, synchronous communication. It does provision for async communication with server storage of offline messages, and even originally discriminated "chat" messages from "email"-type messages with multiple recipients and a subject. IIRC, this latter feature is deprecated as the protocol developers focused on real-time stuff. Because in the end, and despite all its kludges, e-mail doesn't need replacement. Its biggest problem remains spam, and even that is under control by all the major providers.