I'm right handed, have worn a watch off and on for 20 years and always wear it on my right wrist when wearing a watch. In High school and college, I had a pocket watch, wore it in my front right pocket so that I could check it with my right hand. Works for me.
As for the Watch VS Cell phone, I'll take the watch any day over a cell phone for telling time. My watch is over 5.5 years old and still on the same battery as when it was new. My cell phone lasts 4 to 6 days between charges. If I'm in the woods, my phone is off, so I'd need a watch to tell time and time what I'm cooking. Back when I worked for someone else, I couldn't have a phone on the sales floor, or in a meeting, but watches were fine. No phones at the Theator either, so a watch is needed there too. There are times when you don't want to be reached like at meal times or when out and about, but you still want to know the time. Take the watch, leave the phone at home or in the car. My watch goes anywhere with me, my phone, not so much.