I went to a national park with my GF to watch the recent Perseid. There was no phone signals there. Except for the map, I didn't need it so I didn't care. At multiple times though I reached for my phone to Google questions we were asking ourselves, on nature and space. I guess in a way it pushed us to think more about the subject instead of getting an instant answer, so in a ways it's good, but we never got any actual answers, we just forgot about theses questions though, which I don't feel is good...
I'm running a business on my phone, so for me - yes. If I pull out my phone to take a photo on a Sunday and I see that a big client emailed into support, I'll get distracted and feel the need to respond quickly. Monday through Saturday, this is the proper reaction - so I need at least one day a week to disconnect and enforce more strict boundaries.
If that isn't only SMS messages you likely use it like most do. Facebook, Instagram, Snapchat, WhatsApp, etc. I don't have a phone off day but I don't use any social media on my phone at all. I do believe anyone who does could use some time off because it is an addiction and most are addicted. Using it with other people around really should be frowned upon. Like back in the day when you only called people on the phone after 9 and before 21 and not at eating times. It is bad behavior really.
Speaking about myself, I only have notifications for emails and for messages directly addressed to me. I might check it occasionally on the bus to see what popped up in the news but other than that, I don't have the need to pull it from the pocket all the time.
What exactly do people do different than this with their phones? I really feel that I have been missing something amazing with the smartphone usage when I read posts like this.