With a $20 antenna placed near the window, together with a modern receiver, it is easy to get nanosecond level of precision for GPS systems. Some receivers even have in-door precision specification.
GPS not only work indoors, in terms of timing, it works actually pretty well indoors.
There's no need to 'solve' for time - it's included in the raw data packet from any single satellite.
As any 'solution' carries an inherent error margin, the desire for an excess of sats doesn't stem from solving for time but the reduction of error.
https://www.e-education.psu.edu/geog862/node/1724
Edit: I would welcome corrections though if I am misunderstanding. Perhaps if you're not interested in precise timing you can read the satellite time from the broadcast signal?
Edit 2: OK, I think I understand your point now. The satellites broadcast their timestamps directly. To find a precise position / time you need to find a correction to the receiver clock. But if you don't need a very precise time, you can just use the satellite timestamp.
the GPS module itself is probably bigger than most of these watches, and the module itself probably costs more than most of the watches too! (probably something like $100). even if you can power it, which, the power consumed is probably 3-4 orders of magnitude more than the watch.
on the other hand, you have a point about receiving a signal and setting the clock, and I wonder if you couldn't parasitically drive this off the cell network... is there a local reference clock signal in the cell system that you could pull timestamps from and set the clock? cell signals are much much stronger than GPS and don't require constantly tracking satellites to maintain a fix. and while you still need some RF components (as does this casio watch, it's still acting as a RF demodulator!) they can presumably be much simpler and cheaper and lower-power.
(edit: actually I see some people here commenting some watches apparently do exactly this, so your "use the time reference from a single satellite and accept the skew from lightspeed" idea probably does work, although it's a smartwatch and runs its battery quickly.)
really I think most people do not even need continuous updates though. This is something you could build into a "charge cradle" for the watch and have the time reference sent via a data carrier on the inductive charge signal. which does open GPS sync back up a little bit (although wifi/bluetooth would be cheaper and just as good for most people) since the GPS can live in the cradle too.
people are talking about solar watches etc and to be honest if you've got 1-2 years of battery life who cares about solar? Pop it on the charge cradle once a year and charge it inductively. Inductive charging might actually be simpler/cheaper than even those micro solar panels watches and calculators use, and everyone has gotten into the habit of charging their smart watches overnight anyway. And if you do that, it allows you to do the cosmetics of the watch however you want, since you're not tied to having a big solar panel in part of it.