The real question is why do we invent push notifications schemes when we already have SMTP? What is a notification if it is not a small ephemeral mail?
You literally get notifications mail in the physical mail box... And you get notifications and alerts in your email too, like payments reminders, calendar reminders, and all sorts of ephemeral notifications and reminders.
Not sure why do you think you need something other than SMTP to solve this problem once and for all.
