What are the "cons".
Of course you should keep records. In addition to serial & model number, caliber, finish, etc etc, its a good ideal to have pictures.
Make more then one copy and put them in different places, including a safe deposit box.
In the early 80s I got burglarized. 23 pistols/revolvers were taken. I got 20 back, two I didn't recover were thrown in a lake. Only one was sold by the bandit to a stranger who we never found.
All because I had good records.
This advice is not just for guns, but everything of value. If it doesn't have a serial number then engrave your drivers license number on it.
When I was in LE we had to sell at auction, or destroy, thousands of items we recovered simply because we couldn't trace the property back to the original owner.
I mentioned engraving your driver's license, many people use their social security numbers. Guess what. You call the SS office to find out who the SSN belongs to, they wont tell you. Even the police trying to return property, its a privacy issue. No where else does privacy matter unless the cops are trying to return your property. Cops can always find out who owns what drivers license.
As a side note: If you do every thing you're suppose to, record everything, and something is stolen, and returned, make sure you check to make sure the stolen property is cleared from the records, including NCIC, (the Feds).
When I was running the AK NG Rifle team, we flew to Arkansas to shoot the NG Championships. We had a M14 rifle stolen in route. Of course I had all the information on the rifle and reported it to the FBI, local police, and my boss in the Alaska NG. We had a spare rifle so it didn't interfere with the match. This was in the late 80s.
Good News - Bad News. The rifle was recovered, found in Little Rock, taken by some idiot baggage handler. So comes the bad news. The same rifle had been reported stolen in 1968 and never recovered. Of course it was recovered, it was on my property book, But wasn't recovered per NCIC.
No problem with the FBI, I had an alibi, in '68 I wasn't in Alaska, I was in Vietnam. However, military paper work being what it was, a SIR (serious incident report) and investigation was started. Lots of jumping through hoops, all because someone forgot to tell someone the rifle was recovered.
KEEP RECORDS, I see no CON about keeping records.