I think all these systems end up being abused and users just stop paying attention to them. The reason is, google doesn't have a vested interest in notification

I think all these systems end up being abused and users just stop paying attention to them. The reason is, google doesn't have a vested interest in notifications being great. Facebook didn't either when they had their platform, so it was full of spam and ended up being useless. I think the same is happening with browser notifications. Mobile notifications seem to be going on the same path of saturating. What i find more useful is to have the notifications in-page. If the user wants to keep a tab open, they ll hear a beep when something interesting happens.