Actually, a reliable analog watch can serve as a compass if it's anywhere near accurate.
Point the hour hand at the sun, and the 12 o'clock points surprisingly accurately south. (In the northern hemisphere, daylight savings time notwithstanding.)
Watches are my "other" fetish, after guns; but whether a watch would be important post-shtf, can't say. Probably not life-critical equipment, so I'm not getting into that argument other than to say there could be times it would be useful. Either to coordinate some action with someone, or even just to KNOW you waited a half-hour after that patrol passed before coming out of your hole, rather than "thinking" it's been "about" a half hour.
That said, main problem with watches in a "total collapse, long-term, mad-max post-shtf" situation is that you have to trade off accuracy for useable lifespan; no way around it. A battery operated watch is much more accurate than a mechanically-driven one, even a high-end mechanical one. Even if your mechanical watch is a Rolex (all Rolexes are mechanical, not quartz), it's only certified to 2 1/2 minutes (150 seconds) a month accuracy. Even a much lower-end quartz watch will be MUCH more accurate than that; generally on the order of 5-7 seconds a month. My battery-driven Omega (which is less than half the price of a Rolex) only gains right at 2-3 seconds a month. And again, that's using a "top end" Rolex mechanical's specs; a lower-end mechanical watch will have much sloppier tolerances.
That means that even a Rolex will be off by a half hour fairly quickly, and even if you do try to adjust it on say, the first of every month, it's still going to just get worse & worse as time goes on.
On the other hand, a battery-operated watch would be basically limited in lifespan to the battery currently installed when the shtf; post-shtf replacement isn't likely.
My thoughts? I have high-end mechanical and quartz watches both, and almost never wear the mechanical anymore. I like knowing that it's "two o'clock", not just "about two o'clock". Lithium batteries can run an analog watch for 5-7 years (and a digital watch for up to 10 years); so having a new battery installed every couple years would mean the current battery always had at least 3-5 years' life left if replacement became impossible.
As much as I hate plastic/rubber watches, the Casio G-shock is darn near indestructible, water proof to deeper than I'll ever go, weighs probably a fourth what the Omega does, costs around fifty dollars, and being digital, has an 8- to 10-year battery life. If I were going to Iraq next week, it would be either the rubber G-shock or the stainless Luminox I'd be wearing; most likely wearing the Luminox with the G-shock packed away as a spare. (I really, viscerally just about hate black rubber "sports" watches, but they are undeniably practical.)
Nowadays it's the battery-driven Omega 95% of the time, with the TAG-Heuer for rare dressy occasions.
Again, is a watch really "must-have" post-shtf gear? Certainly not the highest priority item, but for certain things it would be useful.