I think it is mainly paranoia. Watch collectors paranoia! If the collective do it we follow like sheep! I don't think knowing the serial number of a watch gets you any closer to recovering it. Some proof of ownership would be required to corroborate your claim and Omega don't have any stolen register. I guess if the watch was expensive enough someone could engrave a bridge to match and duplicate your extract of the archives?
The only real reason that makes sense is that it keeps the watch fresh to market, not traceable across the net as being passed from pillar to post.
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