Silly question maybe: why use this at all when you already have a well known, decentralised, vendor-independent, almost real-time, and persistent notification system at your disposal? I'm talking about email of course.

Email notifications are dependent on whatever push notifications your email app are using. Either it's set to reach out and check for new messages at a set interval or use a service like bluemail where you hand over your credentials and they send you a proper push via APNS or Google. Either way not as reliable in my experience.