It's by no means a waste of time, it's your best way of proving ownership. As a street crime, this is likely to have been a crime of opportunity, whereas your example of the Panerai was someone targeted leaving a watch fair - in the former example, the culprit is unlikely to have access to cases to exchange. And the earlier the watch can be caught "downstream", the more likely the serial number is to be intact.

A watch's serial number is more like a car's chassis/engine number than it's registration plate; eventually it may be exchanged, but if it can be found soon after the theft, having the information to hand will make identifying it as your watch easier. Some insurers will let you register serial numbers of specific items as part of your household contents insurance, which could be worth doing if watches are kept at home.

It's all about giving yourself the best chance of recovering the item. Yes, of course it's not foolproof, but it's not a waste of time at all either.