The only reason I can think of why I would send in a perfectly running watch, is the integrity of the seals that keep out water or just debris that may work its way into the watch. Also be sure that all the spring bars get changed to avoid a corroded spring bar from breaking unexpectedly on you. So if you just want new seals and spring bars, then you could possibly have this done by a qualified independent. But if we are going that far, why not have Omega service the watch and hopefully it get's returned looking like new.
Well, that may be conceptually true and yet not literary true since it is the looks what is not covered by Omega's standard fee.
Excepting polishing, hands and crown, they don't include aesthetics so dial, case, bezel, bracelet... the parts that most notably impact the "like new" perception... are not covered.
And then, polishing depends a lot on the hands that will do it and it's not something that can be repeated forever, so no wonder some people will explicitly ask
not being done.
Even regarding hands things are not black-and-white. Vendor's rationale is that they can be damaged on servicing but then, you either end up with hands that don't match up with dial appearence or they do, but then they fail the "like new" test.
I.e.: I recently sent my Speedmaster Mk40 for service; they of course replaced the hands but, given this model has been out of catalogue for quite a long time now, I suspect the hands are also NOS from back then and their lume, while not bad, is no better than the one from the hands they retired (and quite lower than when the watch was fresh new).
Also, the most beaten-up looking part of the watch was the bezel and the steel outer ring that protects it... the bezel was not covered and the steel ring is part of the main case and so thin they couldn't polish it without making the remedy worse than the disease. I have to say the polishing work on case and bracelet was, to my eyes, outstanding and yet, because these things the watch certainly doesn't look "like new".
Also any movement updates they have done since your watch was new may be incorporated into the service. That doesn't mean you get a new movement it just means any parts that changed specs while this watch was in production, might be changed out. They usually change the hands, they offer to change the dial, and unless you tell them not to do it, they will polish the case, and the bracelet polish may be an additional fee. The last time I sent a watch to Omega they polished the watch. I recently sent a Tag Hauer for service and they don't polish the watch unless you ask them to. Just verify with Omega Service what is included.
Again in my case, case and bracelet polishing were included, but I never heard about dial being included. Movement updates I think it's great, except for maybe those most interested in the "historic value" but visible parts, it's a different issue, since they don't usually get upgraded because of quality reasons but economics/stock reduction which usually means they are less valuable than originals, i.e.: you won't get the "Naiad" poligonal crown on your 60's connie but a generic one, or the arrows will look slightly off-looking since they won't be the ones designed for the watch, etc.
Finally, about the main question, I was gifted my Mk40 brand new in 2007, and it went without revision till 2020 because it started to behave "funny" (for most of this time it was almost exactly 3 seconds slow a day and in few months it progressively started to lose more time: I took it as a hint the watch was asking me for service). But starting some two~three years before that I was starting to worry about its water tightness (I used that watch in any condition, including showering, bathing, "light" free-diving...) so I got a diver's for "heavy-duty water-related activities".
Makes it "economic sense" waiting for so long (forgetting about water-tighness)? Well, I think there's an important hint I took from my watch's servicing. They returned to me the parts they alledgelly changed (I think that's mandated by EU regulations) so, after 13 years of faithful and basically constant service, how many parts they updated from that caliber? Exactly ZERO.
I got back arrows, some bracelet pins, crown and stem, chrono buttons, seals... but not a single part from the caliber itself so, they either get "sloppy" and don't pre-emptively update parts unless they go out of spec, or the parts are sturdy enough that under standard use conditions they can last much longer than their advised three-five years standard service intervals, in any of these cases I don't see the value of paying 600+ bucks any time sooner than when the watch starts acting funny for the privilege of... nothing.