I consider it paranoia.
There's a theory that someone could duplicate the serial number on a crime gun or claim ownership of the firearm.
I've never heard even a rumor of a case where such a thing has happened. Plus even if it did, proving that you are the rightful owner of the gun or that it was not used to kill someone in Baltimore while you live in Las Vegas would be an easy task.
There is no "benefit" to having the serial number in photos except for the fact that it requires some level of effort to remove it and I personally feel no compunction to go to that effort for no legitimate reason.
Besides which, there is software available that can "undo" your removal, which seems just as likely to me as someone trying to use the number in the first place, near zero.
Besides which, even if there were actual, verifiable cases of deliberate misuse of a serial number, there are SO MANY tens of thousands, probably millions, of pictures which include the serial number on the internet that the odds of yours ever being used are near zero.