The intent behind a gun registry is to empower courts, and potentially police. A judge would be able to identify that someone owns several more guns when considering whether to grant bail for an armed robbery, and the surrender of those weapons until trial might be a condition of bail. It might be useful information for a judge who is crafting an order of protection in a case of stalking or domestic violence.

Similarly, police who are serving an arrest warrant might be able to serve the warrant with the knowledge that person of interest has several firearms on the property. Sometimes police know this today, but not because of government records.

(I'm not arguing a personal position one way or the other, just explaining the rationale.)