Clients can tell the server to only send important traffic (=when new notifying messages are incoming) before going to sleep so it doesn't use any radio now. Fast reconnects are also possible now, so we can wake up only when a push notification arrives. The only thing stuck in the 90s is your knowledge about XMPP.
XMPP needs a connected network socket which is pretty bad in a time of mobile services. The 90s are over.
Clients can tell the server to only send important traffic (=when new notifying messages are incoming) before going to sleep so it doesn't use any radio now. Fast reconnects are also possible now, so we can wake up only when a push notification arrives. The only thing stuck in the 90s is your knowledge about XMPP.
I know enough about XMPP or earlier called Jabber to not to run it anymore, after years of self-hosting Prosody.
Well, apparently you don't since you're spreading outdated myths.