Yes, almost no one needs a watch to tell time. I counted the clocks in my house a few years ago, counting anything that displays the time as a "clock" including things such as my microwave oven, my stove, computers, phones, tablets, DVCR, thermostat, TV, etc, and found something like 20.
But no, there are still functional reasons to have a watch. I do not want to deal with keeping all the aforementioned clocks actually set to the correct time. Some aren't a problem, such as computers and phones, because they automatically sync to time servers over the net.
With a watch I can reduce my clocks to those on my computer, phone, and tablet, and my watch for when I'm not using those, plus any clocks on things that actually need the correct time.