I have a personal property policy with USAA. Its to insure SOME of my firearms and the wife's shiny items. I do not recall off the top of my head if I had to provide serial numbers or not. To be honest, I do not see what the issue would be if I did. Your insurance company already knows a lot about you. And what would be the reason not to give it to them?
Anyways, my home owners policy covers up to a certain amount for firearms. My collection's value goes beyond what that value was. I did not have to provide any info on the firearms for the basic home owners policy. For the personal property policy I did have to list detailed specs for each item to be insured. I set the value for each item I want it insured for. Keep in mind, if your items are ever stolen, broken, or lost and you make a claim, then you may have to provide proof the items are really valued at what you claimed. Example would be if you listed a Bushmaster AR15 at $4000, you would have to provide a reason for that value when you can walk into the store and buy a new one for $600. I used my receipts and what it would cost to replace the items at the time I got the policy as my values. And yes my policy does cover everything such as accidental breakage or if it is lost.
I basically only have what I consider my higher value weapons insured under the personal property. BUT I am starting to reconsider having everything on the policy that I currently do. I've had the policy about 4 years now. The cost of the policy over 4 years has exceeded the value of about half the firearms covered. I am thinking about reducing the firearms I have covered to just a couple that it would be difficult to replace and the one time value to replace would hurt my checkbook. Example would be my $4000 Bushmaster AR. To me it all comes down to cost of the policy each year Vs. the cost of the one time replacement cost for items plus the likely risk of anything ever happening.
Just my thoughts and opinions and how my policy works with USAA.