I think there will always be demand for mechanical things (see the not-so-recent resurgence in vinyl that doesn't seem to be going away), especially as people seem to be increasingly hankering for the physical in a digital world. Apparently Gen Z (the ones now making Millennials feel old) are increasingly avoiding tech, social media, etc., as they are feeling its negative effects most acutely. I have a 21-year-old son, and he mostly avoids technology, and only has social media for his music projects. The same is true for most of his peer group. (Except video games, though even there they're much more interested in retro or homebrew games than they are in the latest AAA titles.) I think they know better than us how the guarantee of obsolescence within a few short years delivered by modern tech is truly empty and only leads to a treadmill of consumption with very little payoff.
As a very late GenX-er, I like mechanical watches partly because they are old technology and therefore represent a kind of timelessness. I also listen to records, play old basses and like old cars. While I can appreciate quartz and other methods of timekeeping, there's something deeply satisfying about being able to actually see all the parts working together to spin the hands, rather than it happening on a microscopic or even atomic level in chips and transistors. There's also a form of joy that comes from the process of using and maintaining things that require a bit more effort.
For example, the experience of listening to music is totally different when it involves finding the record you want to hear, pulling it off the shelf, admiring the artwork, opening the dust cover on the player, carefully laying the record down, brushing it, and then placing the needle. Then having to flip and change every 20 minutes or so keeps you close and present, as opposed to popping on a playlist and having the music vaguely in the background as you get increasingly distracted. Some may see that all as just an unnecessary irritation, but for me it's a ritual that is akin to a Japanese tea ceremony or making a good carbonara with the exact same ingredients every time.
Winding and carefully setting the time and date on a mechanical watch makes me interact with it on a different level than a smartwatch I just yanked off the charger, and it's a heck of a lot more interesting than trying to puzzle out why the Bluetooth won't connect. Sure, I can pull up time.is to know the time down to the millisecond (and do when setting my watches), and even my best movement is a couple of seconds fast or slow over the course of a day, but I have yet to encounter a situation where that actually matters.
A nicely designed and made watch is also a thing of beauty, with art and craftsmanship combined. Each has its own style that, as jewellery, can complement how one presents oneself (or detract, if done poorly - I think this Invicta may be the ugliest thing ever made under any circumstances:
Invicta Masterpiece Chronograph Automatic Brown Dial Men's Watch 44573 ). We may live in a pajama-pants-in-Wal-Mart society in North America, but again, I like the satisfaction that comes from taking a bit of time to assemble an outfit that shows respect to the rest of the world.
Maybe all of the above is my subconscious way of trying to articulate (read: justify) to my wife why I've bought three watches and a few bracelets and straps over the past few weeks...
TL;DR: Mechanical things are cool, screen phones aren't. Watches are also beautiful, and I like doing things that take time. So there.
Oh, and Rolexes may hold value, but so do many cheaper watches if you buy at a discount from MSRP or used, and many other luxury brands appreciate about as well as a BMW. There's a number of Seikos that have appreciated massively over the last 10 years, but going from $300 to $1500 isn't as compelling as it is for watches costing 10-20x as much.
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