Some people obsess over being constantly in contact with other people.
But some people have a loved one who is in the hospital with serious problems, or is near death, and they don't want to find out that loved one died 24 hours ago because they forgot to turn their phone on.
And some people need their cell phones for text messages because their employer strings them along with changing work schedules. One woman I know of sometimes gets a text message to come in an hour early the next day. She cannot risk not getting the text, as the company has laid off more than half the work force since 2010. She is over 55 and it's not easy for people like her to get another job with the same or higher pay.
To you being at work means losing connection with the outside world or being fired? You should seriously consider finding a new job. Would vibrate or silent pass muster with you, or is it an insta-fire deal?
I would guess that there are a minority number of positions in the world that require not having a phone either on or on your person. The only one I can come up with would be corrections officers seeing as how phones are frowned upon in prison.
They keep calling my cell phone and I don't answer it. But when I call the number back it ststes the phone number has bee disconnected. It's a pain in the butt.