Anything you put on your body that is visible to the public affects how people see you. Whether you care about this influences if you think a watch is fashionable or purely functional.
But when it comes to utility. A simple watch has not been replaced by smart phones yet. That is because there are places, instances and people where/who just can't pull out their phones and check time.
But that didn't cover all people and all use cases. There are many use cases where you can't use your phone to check time. And in such places a wrist watch is a indispensable utility.
It is pretty funny how you continue to bring up timekeeping as if you believe that matters.