Thats defacto gun registration- and worse: registration with a private entity not beholden to due process. Given current realities, anybody who registers their firearm in such a manner can expect a no-knock raid because they were nearby when somebody phoned in an engine backfire as a gunshot.
So make it allowed that the insurance is tied to the gun. You buy a lifetime policy for that serial number, provide payment, and you're done. Payment can be provided anonymously at a window in cash, if that's your thing.
If you want discounts because you live in a low-crime area, have a gun safe, have many guns, etc. then obviously the storage location for the weapon needs to be declared to the insurance company.