Am I reading this right? If WhatsApp and similar are no longer able to implement End-To-End crypto because they have to use an Apple API which supports only specific protocols, this is going to be a huge loss for users. I've considered switching to an iOS device, but stuff like this keeps me away, I'm very glad I can keep direct SIP, SSH, IMAP and XMPP connections open at all hours of the day.
Not being able to lurk in the background does not have anything to do with security. I don’t think Signal uses it and they’re generally considered secure. You can check out their source.
If you would use the custom notification handler you are required to show a notification, which is fine for a new message but doesn't make sense for read confirmations, "is writing" updates or all other types of information that should not pop up to the user immediately.
Of course you can work around it by using a WebSocket while the app is open and only use push notifications for new messages but obviously that's going to be less tight than the current situation.