For the record, I do have a smartphone. It is possible to own one without looking at it constantly.
As do I, and it mostly stays in my briefcase, or my jacket pocket, except for the odd call or text. I almost never use it otherwise, as a proper-sized screen and keyboard is a far easier and more efficient interface to obtain information from online sources.
I wear a watch, because I like them, and, as someone else pointed out, having a watch means I'm not pulling out my phone just to check the time and getting distracted by the shiny. That would be a regular mechanical watch (well, one with a quartz movement, not a strictly mechanical watch in the afficionado's sense), not a smart watch. I see my relatives being continually distracted by the smart device on their wrist, often rudely interrupting our conversation to feed the beast. I have no desire to have such a thing that needs my constant attention.
I also use a printed schedule book, and hand-written to-do lists. I never need to worry about the privacy of that information, my device being charged, the screen cracking and rendering it illegible, or any of the litany of untimely maladies that can befall a fragile electronic device, the operation of which you fundamentally don't own.
You can call me a luddite, and I would not object, but I would also point out that I do accept modern devices into my life; I just limit their reach to what benefits me, not some corporation. Finally, and importantly, I don't automatically assume that just because something is new, it is better than what it purports to replace; I've seen enough to know that is often not the case.