Manners / Politeness, etc are a part of human behavior and usually transcend cultural boundaries. Sure, they vary and differ, but every society or culture has some conception of them, and I'm pretty sure that's always been the case. Watches are a material object and probably were invented out of necessity, just like clocks were. So yeah, frankly I think it's stupid to put manners at the same level as material objects. But I do realize that material objects, i.e., proper clothes and things become a part of manners and that they are important. I'm just saying it's *****ic to take that to extremes. Especially on this forum, which is devoted entirely to getting into medical school.
The watch says you can tell time with class. This I guess depends on your definition of class. Class is a pretty subjective idea. What is or isn't classy is debatable. I think I generally would agree with your ideas on what is / isn't classy. I absolutely think it's classy to wear a watch. So what? You're supposed to be professional at your interview, not classy. Who cares. If you're interviewing in an institution where dressing classy might help, then go for it. If I were to interview at a bank, investment club, corporate HQ, political office, I'd probably try to be more classy. Medical schools won't care as long as you are presentable, dressed appropriately and act professionally. That's all.
I am not a utilitarian, although I do tend to focus more on the utility of things. Your problem is you argue at extremes. You ask why we have music, art, architecture, humor etc, when there is clearly no absolute utility for them. However, nobody questioned why they exist, or should continue to exist. And we're totally cool with your fascination and dedication to the art of dressing well. Just don't expect the rest of us to be all giddy about it. Most people here just want to know what will get them through the interview without being considered unprofessional. And I am 99% sure that lack of a watch will not cause any such problems.
I guess the point I'm trying to make is, I like the middle ground. I'm not going to bend over backwards to be considered classy at an interview, when clearly the purpose of the interview is to showcase other talents. However, I would recognize that being classy to some extent would help make the best impression possible.