Notifications are incredibly useful but only when the information is important. You wouldn't want the bat phone on silent, but you also don't want it ringing to be sold insurance.
I realised how badly my notifications were configured when a comment on Facebook caused my phone to ping and two computers to make a noise. Thats a lot of attention. So that's an email sent an a push notification to my phone.
I've started to reconfigure all of this because of the level of annoyance. The problem is that the levers that I have to use are all a bit unsubtle. Email or not, notify or not.
What about importance and engagement? I'm not talking about AI a few simple rules would do it, they actually manage it pretty well with the feed. Can't be hard to detect if I'm actively engaged in a conversation or just chiming in to cause trouble.
The intelligence doesn't actually have to be in the service that your interacting with there could easily be a middle man service that you forward everything to. I would have to work out two things, the importance of the message (hard) and where you are.
If its important sent a push and have it make a noise, make of note of whether I have seen it. If I havent make sure that it shows up when I move to a different device. For less important information queue it up into a feed that can be looked at later.
This isn't a spam filter, its something more I think. Google are getting there with voice which does part of the job, maybe of Apple could come up with a similar service and roll their push notification into it that might get half way there.