Some people feel that a BOS will protect them if a firearm they sold was used in a crime. Bad guy buys gun and of course uses his real name on the BOS. Bad guy shoots up a bus load of nuns and orphans. LE traces gun back to seller. Seller waves BOS and all is well.

Personally, I never require a BOS for a sale and have only ever had one seller ask for one.

As far as proof of ownership goes, just take a pic of your firearms (with serial #s) and keep in a safe place.