If your life is significantly "digital", if you're interacting with people constantly via email, twitter, messaging apps, etc. then you're going to have a lot of notifications every day. And cutting out the "few seconds" of hassle to pull out your phone and check those notifications is a significant savings when multiplied over all those interactions throughout the day.

As for battery life, my pebble time steel lasts about a week between complaining about needing charging, which is at about the 35% range, where it could survive probably several days of use if you forgot to charge it. And if you have a smartphone it's probably not a significant inconvenience to add another cable to your charger one day a week overnight.