I had two lost items returned to me, a light meter and a calculator, only because I had put my name inside the battery compartment with dymo tape, but both were found by people who knew me.
Roger is probably right, but I had a friend whose car battery was smashed. He put in a new one, and the thieves returned to collect that the next night.
The police recovered the battery when they caught the guys, but because he had not marked the battery, they refused to return it, they told him he could bid on it at auction.
Same with money, if someone steals your money and is caught, can you identify the money? You might fan out the bills and snap a digital image with the serial numbers, easy enough. Might get a bit tiresome if you take singles. ;-)
Distinguishing marks on jewelery and other items may be of at least as much use in recovery as a serial number.
I found there was so much theft in Prague one summer, I personally saw people selling or trying to sell, stolen property three times in camera shops and an antique shop in one month.
If you call my ten year old Czech phone number, someone will answer, in Russian. Guy never changed the sim card.
Regards, John