Seriously, if your daily activities require actual thought, turn all that shit off. If you need to know when a critical email shows up from time to time or from specific people, find a tool that does that or wire one together yourself with IFTTT and a push notification service. Your flow will thank you.
What would be handy in a tool like this is being able to set up what I described above; normally don't ever notify me, but allow me to turn on real-time notifications for particular people on demand, or other rules for knowing when it makes sense to interrupt.
[1]: It was originally called Gmail Notifir.