Nothing about matrix or xmpp is “ideal”. This person knows nothing about how notifications work on iOS.

I think they focus mainly on the fact that these are federated and mature solutions. I don't know anything about Matrix but as far as XMPP/Jabber and "push notifications" go, you don't need to reveal the message, nor the sender, in the alert. Right, it's not perfect, but in my book that goes a long way for privacy.