First, [at work,] there were usually clocks (synchronized, atomic clocks) at various points all over the place. Turn your head and see what time it is, often to the shared second.
Second, usually, other people attending meetings would tell me that there was a meeting in a half an hour, then they'd say the meeting is in fifteen minutes, then that the meeting is in five minutes, and finally, "Are you going to the meeting?" I don't need a watch for that.
Third, I usually left my phone in a secured box outside my building or in a box outside the work are that was inside the building. Remember to turn it off! Nobody wants to hear your crazy ringtone draining your battery!!!
At home, I have wall clocks or time displays on various appliances, the computer, etc. so I don't need to have a watch or cellphone to remind me of the time.
In the car, there's a display on the dashboard. It's about five minutes fast and I haven't reset it. If I'm in my car to get somewhere, the time is going with me.
My first job as an officer was one where "We count every minute because every minute is counted." My organization had watches made with the unit emblem and gave them to people. Whenever I wore that unit watch...things broke. People asked me not to wear that watch or to take it off if things weren't going well. They'd even ask, "Ma'am, are you wearing your watch?" if they couldn't fix a problem. When I came into meetings, I was usually swept along with the warrant officers, so I wasn't late...just part of a gaggle as I took the most junior warrant officer slot in "Warrant Officer Row," the top row in one of the briefing rooms. We weren't late. We were...fashionably storming the meeting.
Now that I'm retired, my time is largely my own. I do have places to be at some fixed times, but they work well at an "I'll get there" pace. The events last as long as they last and I try not to pack my schedule like I did when I was working.
I do have some alarms on my cellphone, but they're mainly for feeding the dogs or prayer reminders.
[Where I used to wear a watch, my left wrist, I now have a rosary bracelet.]