Comment by matthewdgreen

Getting rid of all metadata is fundamentally hard, unless providers are willing to deploy PIR or anonymity networks. But I think it's a mistake to assume metadata means "just the timing of a message": these push messages may include a lot of detailed content that is being described in this article as metadata, and all of that stuff can and should be encrypted.

Additionally, with a little bit of work (well, really quite a lot) the push messages can be made to hide the source. This would make it harder to distinguish a Gmail or DoorDash notification from a WhatsApp notification.