That's three right off the bat, and I haven't worn a watch for 20 years. I am sure an actual watch owner will have more.
To paraphrase Darth Vader: Do not be too proud of this battery powered wonder you have rented. The ability to diagnose medical conditions is insignificant next to the dark side of a month-long international trip.
I keep time accurately with my GPS time synchronized cell phone. The watch is for show, literally. Some of them are amazing.
It seems quite difficult to make the case that the mechanical watch is superior in terms of human ingenuity, manufacturing / supply chain sophistication, or sheer number of "clever tricks," but I'm not entirely comfortable with the explanation that it's just a status symbol that gains its value from exclusivity or brand.
Your microprocessor is obviously much more complex, but there's no observable operation to marvel at. There's no visceral awe component.
First, check out this video. Personally I think the watch is ugly as hell, but if anything shows you some of the craftsmanship that goes into a watch, this would be it: https://www.youtube.com/watch?v=yIXPplShtg0
Another reason is that I'm a programmer and clockwork is a form of programming. I don't know much about watchmaking (I'm hoping to eventually go to watchmaking school - not for many years though I imagine) but I read quite a bit about it and it fascinates me. It's similar to how the idea of programming on an incredibly old computer with practically no resources fascinates me. Complaining about only having 2K of memory? At least you've got electricity!
There's a hell of a lot of invention and, well, hacking that goes into watchmaking too. Take the perpetual calendar, for example - a type of watch that only needs to be adjusted once every 100 years because it tracks leap years. Moon phases that are accurate for 5400 years[1]. Planetariums on your wrist, all powered by clockwork[2]. Dials that take a century to complete a rotation.
I also love the human aspect of watchmaking. The level of craftsmanship in a high end watch, such as the Patek Philippe you saw in the video, is incredible. I love the attention to detail and the care that goes into every single component: even components that are buried deep inside the watch are still polished and decorated by hand. Pointless? Yes! But I can't help but love it.
You mention supply chain sophistication and you might be right - but don't think that the supply chains for watches aren't sophisticated. If you're interested, Hodinkee.com recently published an article about their tour around the Rolex manufacture. You might be interested in the level of complexity: http://www.hodinkee.com/blog/inside-rolex It's a long article but if you search for "Parachrom Hairspring", that section will give you a bit of insight into the kind of invention that goes into modern watchmaking.
However, after all of that justification, I'll fully admit that it's pointless. A $100 quartz watch is typically more accurate than a $10,000 mechanical. It's pretty much all about emotion, similar to how some people can become attached to paintings where all others see is paint on canvas.
[1] http://monochrome-watches.com/a-worlds-first-christiaan-van-...
[2] http://www.vancleefarpels.com/us/en/article/10935/midnight-p...
(Hm, I wrote quite a bit more than I intended to and must have given you at least an hours worth of reading/watching material! Perhaps I should write this up as a blog post sometime.)
That said, after getting into repairing watches, a well made mechanical watch is something to admire. Plus, it's the ultimate recyclable. It is something you can pass down to your kid. A rose gold Rolex bubbleback from the 50's looks and feels great on the wrist--even if bought second hand off ebay. My only concern when wearing a nice watch is theft these days. I guess it's like driving a Olds 442 convertable vs. a Tesla? I can't compare the two. (I have never driven a Tesla though, but I have been in expensive cars)
That said I don't see much difference between the quality of older watch movements. I can honestly state that I can't see any difference on quality of a Rolex vs. Benrus from the 40-70's.(comparing just movements, not the case or straps)
I doubt existing "dumb" watch buyers will switch over to a smart watch. All smart watches I've seen so far look horrible (incl. the Apple one), in comparison to properly constructed mechanical watches. They also don't act as a status indicator.
(Not that I care much about watches. I do however appreciate the craftsmanship that goes into building a proper mechanical watch.)
All of this leads to expensive smart watches - I have a Microsoft Band for the SDK (I want to try multi-factor authN with it, based on this - https://www.wittenburg.co.uk/Entry.aspx?id=69e92695-f6eb-42e...). Beyond that, nothing. The (few) nice things I have are because they please me - not for their ability to impress others. But then, I'm not wealthy. Maybe when you get there, the outlook changes.
The point is nobody buys a $176,000 watch for "productivity" reasons.
That's why some cost more than your house or car... Its not about 'function'.
A Picasso doesn't compete with your TV, nor does Viannay Halter or Felix Baumgartner compete with Apple.
The same thing happened with the plethora of tablets a few years ago.
This question was answered in the 1970s "Quartz Crisis" : watches aren't about functionality.