Yes, I do.
Clocks are always ubiquitous until you actually want to look at one to see what time it is. Then you're conveniently in a room/area with no clocks.
As for using your phone, you have to dig it out of your pockets. And given the trend toward relatively large phones and relatively snug-fitting pants, that's a rather cumbersome task compared to the less than one second it takes for your eyes to glance down at your wrist.
I also consider it rude to look at one's phone during a conversation with someone. It's easier to discretely check the time on your wristwatch (or theirs).
Yes. Mainly for style rather than time-telling though.
Both of these answers. This is my everyday accessory: