I understand that many people nowadays do not wear wrist watches but instead get the time from their cell phones.
Since I sometimes hide from my cell phone, I doubt if I'll adopt that practice.
I once knew an executive who never wore a watch and did not, in those days, have a cell phone. She relied upon her staff and wall clocks to keep her on schedule. They did a poor job of it since she was often late to meetings. That habit tended to detract from the loose attraction of her renegade practice. Being a rebel is one thing; making others wait is another.
The one compromise that I've made in her direction is to avoid digital watches. I don't want the exact time. A rough approximation will do; one that can be obtained at a quick glance. Since I coach executives and managers, my office has clocks tucked in odd places so I can get a sense of when a session needs to be wrapped up. They are placed so the client cannot see them because I don't want clients to worry about the time. That's my job.
I recall that Napoleon claimed the Austrians lost a battle because they didn't know the power of five minutes. It is jarring to meet people who seem to have no sense of time; who can speak for 15 minutes and swear they thought it was only five.
They might need to go digital.