I'm a huge believer in disabling any form of push notification. Nobody's software is entitled to my attention, I'll use it when I feel like it, not when it nags me for attention like a petulant toddler. I don't know how people tolerate their phones pinging, flashing, and buzzing all day like a pinball machine that's been very personally crafted to extract as much attention from your day as possible.
A little off topic, but since social media seems to be the main driver of this "phones as a personally crafted distraction" I'd love to see what a social network that's not actually deeply antisocial would look like. No push notifications, no filter bubbles, no politics, no "nudge" messaging from governments and other organisations aiming to subtly change people's behaviour, no creepy advertising pushed to a perverse degree. Just give me a place with a good chat client, a way of asynchronously keeping in touch with people in my life in that long range between "good friend" and "stranger" (seriously even the Facebook walls of 2008ish would do), and just enough non-obnoxious adverts to cover costs and make a reasonable profit. Oh yeah, and you should always be able to pay a small monthly fee to be rid of ads if you want to.