Thoughts while shaving----- A good reason for not showing a serial number is that the firearm may be stolen or it has an obscure past and Could be stolen or it was possibly lost by the previous owner and the finder does not wish to be helpful. I just cannot think of a good reason to hide the serial number of a legally owned firearm.
Just playing Devil's Advocate... because a ne'er do well could see a gun for sale on Gun Broker, take note of the serial number, report the gun stolen (from him), provide police said serial number, wait a bit hoping the gun doesn't sell, then contact police again later and tell them he saw "his" stolen gun on GB?
I know... I'm reaching here. Think I need to go shave.