Well, I don't live anywhere near Taiwan, fwiw, and don't think this is about cultural differences at all. I think it's more about defining reasonable expectations, and how one should behave when those aren't met. To my way of thinking, anyway (always likely to be wrong), that transcends national differences, at least on some level.
This is a fascinating conversation to me, and I'm not exactly sure why. But I appreciate all of the different perspectives---they've got me thinking.
What I'm seeing is that this comes down to two questions: 1) what is a reasonable expectation to have of a new Omega watch? and 2) what is a reasonable way for the customer and the seller to close the gap between that expectation and reality when they don't align?
Re: reasonable expectation of a new Omega, I suppose that's very subjective. If you're a longtime collector of super-complicated Pateks, a Speedmaster might be a slum-watch that you nab with pocket change at the mall with no premeditation. You might not even the keep the warranty card for a mass-produced trinket like that, and might not even care if the chrono hand broke after a week.
But many---I'd hazard most---of us approach Omega as a luxury product, even if it is a mass-produced watch from the SWATCH group. For me, getting a new (or even preowned) Omega watch is an adrenaline rush. It's something I have to budget a bit for. I'm tracking the package when it's en route. If I'm buying one new from an AD or OB, the whole experience is special---it's not something I just happen to do on the way home from work; it's something I've been thinking about doing for weeks. And one of the reasons I love Omega is that I do put faith in the exceptionalism that they hype in their branding, re: their "quest for excellence," e.g. (from their own website): "Only watches having successfully passed the most stringent quality control earn the right to reach your wrist."
It's a reasonable expectation that when you save up for and take the heartpounding plunge toward a brand new Omega that costs more than someone else might spend on a used car, you're going to be getting something superlative for that money: a beautiful and resilient watch that will outlive you, yes with regular service intervals, but not an imminent service. To put that last bit differently, if it's a piece meant to celebrate or commemorate a milestone (not that this changes anything, but for many people this is indeed the case), it's a reasonable expectation that you will get to savor the specialness---the occasion of that watch---with several years of satisfying use before needing to part with it for service. (If someone thinks I'm wrong about this, please comment---I'm not closeminded about anything I'm saying here.)
True, as someone else mentioned, issues like the OP's are what warranties are for. There's a logical progression of responsibility/custody that flows from presale to warranty period to post-warranty period: the watch is Omega's problem before it sells; during warranty, the implied agreement is that the watch is now "our problem" (that is, shared by both Omega and the customer, who understands that there may be some inconvenience and disappointment should something go wrong, but no expense); and during the post-warranty, the watch is squarely the customer's problem. But can we reasonably say that in the first week or two of (presumably normal) use a watch that passed through "stringent quality control" should not experience a major malfunction like this? (Maybe during the 14-day return period? I do understand that wearing voids return; I'm just using this as a timespan.) And can we also say that a malfunctioning chrono pusher is different from a hand that doesn't line up perfectly or some other quibble that one can only see with a loupe? We're not talking about getting Holy Trinity level perfection from a glorified SWATCH: we're talking about basic functionality.
No doubt, as far as the letter of the warranty goes, the OP is in the warranty period, and the policy would dictate that he should do exactly what he's been told to do by the dealer. But is that Omega satisfying his reasonable expectation of the brand? I'd say no way. There's a pretty big gap between what this man experienced and what all the marketing (and forum hype, etc) would reasonably lead anyone to expect. If I were the SA or anyone at Omega with the mandate to care about customer satisfaction, I'd want to address this.
Re: a reasonable way for the customer and seller to close that gap. Again, I'd walk back "demand" and say "insist," and I guess it didn't even occur to me that politeness wouldn't be a part of the bargain. (I work in a field where incredibly high quality standards and politeness are both expected, even when giving orders/making demands.) Yes, of course, always be polite, don't be an entitled a@@hole, but also don't be a total pushover and treat Omega with unquestioning gratitude and reverence: you're allowed to (politely) insist on getting what you have paid for. That doesn't make you a jerk. It makes you fair and smart, and may well sustain you as an Omega customer. You can even think of it as magnanimously giving Omega a second chance to live up to their branding.
It's safe to assume the OP doesn't yet have an emotional connection to this particular watch (no?) so he'd probably be happy to accept a replacement, and that's what I'd try to do if I were the SA, regardless of any of the objections mentioned previously. But if that simply isn't an option, then I'd want to ask him "what can we do to make this right for you?" And I'd probably list several easy options, such as a new strap and hardware, a watch roll, a free post-warranty service, a substantial 3-figure discount on another watch, etc, etc. I spent years working in customer service and would say this is 101-level stuff. And if the AD doesn't offer that, then the OP is very reasonably expected to say, again politely, "look, this experience has left a bad taste in my mouth, and I'd like it if Omega provided me with a complimentary ___ to address that." It doesn't involve yelling and pouting like some airline counter customer-baby who doesn't understand how air-travel works; it doesn't need to involve threats or ultimatums. But having some spine and ensuring you get what you've been led to reasonably expect (or otherwise be compensated for any shortfall) is the way to go, IMO.
