This is word-for-word what Notifo was built to accomplish. Maybe with the weight of Mozilla behind the effort (and a large pre-existing install base) they will have more success.
I have the same problem with this feature I had with Notifo: It sounds awesome, until I try to think where I'd use it. I can't find many uses where it would beat email, even though I use it for some things like HN comment replies, notifications for actions on my web apps and various personal events.
I think the area where notifications are important, but slightly less important than email, yet not so unimportant that you don't want to have a user install another app, is pretty small... Too bad, I very much like the idea of Notifo. When will it stop working? Do you plan on open sourcing any part of it?
But it does compete with email, I get instant push notifications on my email client on all my devices. The killer feature of Notifo et al is that you can customize the alerts that will be generated, but that's a small part of what the notification does (i.e. notify you).
