FWIW this is completely reasonable. Push in XMPP works the same way. They way FCM (Google) and APNS (Apple) work is that only the app vendor with proper credentials can trigger push notification for an app. Therefor it has to be proxied through the app developers server anyway. And of course it cleanly separates the MDA from the various, proprietary push solutions.

That sucks, I'd like to involve as few parties as possible in my emails. Right now I just have a direct IMAP connection that it can push over even on mobile.

What about for desktop purposes? What would a proper client like Thunderbird or Outlook do?