WOW. I hit a nerve! Lots of emphatically pro-watch people here.
Don't get me wrong. I'm not advocating that we get rid of watches. They can be beautiful accessories. But maybe this is the wrong place to ask "if watches are over". What I mean by that is, will watches eventually disappear in the future? Will they become quaint, charming relics of a bygone era? Like the pocket watch? You still see those, but they are definitely not mainstream. They have a retro, steampunk vibe.
I would probably get a more accurate answer by looking at young people. Women above a certain age (myself included) were around before mobile phones, and are more likely to have got used to wearing watches. This forum has a pretty broad representation of age groups. Also, I wonder what the response would be if I asked the question to a random group of women (as opposed to women on a fashion forum)? I'm guessing that the average woman here is particularly interested in fashion, and thus more likely to collect accessories and wear a watch for reasons of style.
There are lots of strong opinions about how it's rude to check your phone. Interesting. I don't find it so. If a person checks his watch or checks his phone, I see it either way. Checking your watch is slightly more subtle, but humans are pretty perceptive. Even a quick downward glance at the wrist is easily seen. I do think that texting or web-surfing on a phone can be either rude (if you do it when supposed to be interacting face-to-face with people) or dangerous (if you're driving).