Yes, I cruised last week, and you do not really need your phone after noting your dining rotation and taking a picture of your safety drill location.
1. You can ask for a paper menu in the dining room.
2. You can prepay tips in advance of the cruise, and bring cash onboard to be able to tip extra as desired.
3. You can avoid trying to disembark at ports first thing (getting up at the crack of dawn on vacation is overrated, anyway). Once the first hour has passed, the virtual queue typically isn't needed. And if you've snagged a CC cabana, you can bypass the queue for CC even if you do disembark first thing.
4. You do not need a phone during activities or shows.
5. You do not need a phone to review & order your cruise photos- that occurs at a kiosk at Shutters. You don't need your phone when they take the photos- they just ask for your stateroom number.
6. Activities are listed on the stateroom TV.
There is nothing to stop you from unplugging for your cruise.