I heard one limud zechus is that people wear it more as a form of jewelery than as a tool to tell time. If it’s jewelery, then it’s permitted to wear in the reshus harabim as it is similar to clothing. If it’s a tool, then it would problematic because of carrying. Since most people have a special watch for Shabbos, that might be enough for it to qualify as a jewelery. Though I heard a Rav once say that it’s hard to tell whether it’s more jewelery or tool, and one way to answer up the safek is if the person would be willing to wear his nice Shabbos watch even if it broken and is of no use to tell time.
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