They *can* be a status symbol, but they are not necessarily a status symbol.
I have many watches--some that would be considered status pieces--and wear a different watch almost every day. Most are analog automatic movement watches, so they need to be kept on a winder, or reset if they aren't worn for a couple of days. But I still like wearing them, and I pick the watch based on what I'm wearing. Most of them keep "OK" time, but not like electronic devices, especially those that automatically update to the correct time.
I think it just makes a person look like they're put together, and it completes the appearance. Watches can add a touch of sport or a touch of class to many outfits. They are also very useful when swimming, sailing, and diving, and in many situations where a cell phone would not survive for a moment. Some of them have functions that help you during the day, whether timing events or just showing the date. I use the date display on my watches several times per day.
And personally, I just enjoy wearing them, regardless of what anyone else thinks.