This has crossed my mind too and I have another take on it.
My experience is with classic cars. The fear is that with declaring the serial (chassis) number, someone may claim, rightly or wrongly, that they have the same watch (car). This leads to controversy as others are inclined to take sides and argue in favour of one case or the other. The 'papers' of either may, or may not, be in the correct hands.
Inmy view, watches and cars are a valid comparison. You can build either around a (fake) case or chassis plate and nothing else is original.