For several years my wife and I refused to have a cell/mobile phone, until there was a rather unpleasant encounter. My wife was on her way to an appointment when the train stopped. Net result: 2 hour delay, and late for the appointment. No phones on the train, no way to make contact.
The person with whom she was meeting was incandescent, and entirely uncomprehending of her not having a phone. It was as if he refused to believe that she didn't have one, and thought she was being actively malicious.
So we relented.