Rhea, do we have the same mother? Mine always completely means well, but gets oddly stubborn and specific about Things She Thinks I Need.
I'm in my 30s and have always worn a watch every day for basically the same reasons people have mentioned. I don't always have my phone right with me and, even if I do, it's easier to just look at my wrist than drag the phone out. I like how a nice watch looks as an accessory and, since putting one on is so automatic for me, it's a really low-effort way to look a little more put-together. And Thistle's point about meetings is key! Same thing for any situation where you're counting down the minutes until it's over, but are too polite to want to make it obvious.
I have two watches I wear regularly. One's a delicate two-tone metal one that I coincidentally got a few years ago when my parents (by which I mean mostly my mom) gave me money to use towards a nice, "adult" watch for my birthday. The other is a chunky rose gold Michael Kors one with a very similar face to the second one you linked. It turns out that, once I had one nice watch I enjoyed wearing, I wanted another one I could wear when I felt like something a little more statement-y.
If you really don't think you'll wear a watch, I like the idea people have suggested of gently seeing if your mom might be open to getting you another piece of special jewelry that you'd wear and appreciate more instead.