For me notifications are the main problem, and that's exactly why smartwatches have helped reduce my phone time.
I still carry my phone on me when I have my smartwatch, but even then, it has reduced my phone use. One of the common ways I'd get sucked into my phone was that I'd get a notification, pull out my phone to look at it, and then get distracted by something else. With my smartwatch, I see the notification on the tiny screen, and only take my phone out if it's something that requires a reply/action right away.
Turning off notifications (either for everything or per app) doesn't work for me, because I do want to receive notifications for time sensitive things (ex. "Let's meet at XYZ in 30 mins"), and the classification for immediate action or not isn't based on the app or the sender (one Facebook message might be require immediate action, while another, even from the same person, may not).
It's not perfect; there's still the problem of taking out my phone not due to a notification, but it has solved one major class of problems.