There is now a 17cm3 atomic clock chip on the market for about $2300, well under the price of a high-end watch. I'm surprised nobody's made a wristwatch with that.
Perhaps I should've said "wristwatch formfactor", you're right, battery performance would not approach cheap digital watch, not by a long shot. But at at 120mW, you'd be able to get a few hours out of it with a CR2032 cell, which is better than useless. Garmin made GPS wrist units that up until recently have done no better than this, although admittedly, there's probably more utility in having a GPS on your wrist than an atomic clock.
Your could write "HOURS AND HOURS OF BATTERY LIFE!!" on the packaging.
Because a >>$2300 wristwatch is a piece of jewelry, not a way to tell accurate-to-the-second time. Typically, it will have an intricate mechanical movement and be almost as accurate as a $5 quartz-driven electronic watch from the gift shop.
Absolutely. See Slyde watches: https://www.slyde.ch/
$5k+ for a watch with an LCD screen you can update via software. I appreciate they use high materials in the construction, but the profit margin on these must be huge.
The chip: CSAC SA.45s.